Ages of cable TV shoppers. Refer to the International

Facility layout study. Facility layout and material flow path design are major factors in the productivity analysis of automated manufacturing systems. Facility layout is concerned with the location arrangement of machines and buffers for work-in-process. Flowpath design is concerned with the direction of manufacturing material flows (e.g., unidirectional or bidirectional; Lee, Lei, and Pinedo, Annals of Operations Research, 1997). A manufacturer of printed circuit boards is interested in evaluating two alternative existing layout and flowpath designs. The output of each design was monitored for 8 consecutive working days. The data (shown below) are saved in the file. Design 2 appears to be superior to Design 1. Do you agree? Explain fully.

Problem 1E The purpose of this exercise is to compare the variability of and with the variability of . a. Suppose the first sample is selected from a population with mean = 150 and variance = 900. Within what range should the sample mean vary about 95% of the time in repeated samples of 100 measurements from this distribution? That is, construct an interval extending 2 standard deviations of on each side of . b. Suppose the second sample is selected independently of the first from a second population with mean = 150 and variance = 1,600. Within what range should the sample mean vary about 95% of the time in repeated samples of 100 measurements from this distribution? That is, construct an interval extending 2 standard deviations of on each side of . c. Now consider the difference between the two sample means . What are the mean and standard deviation of the sampling distribution of ? d. Within what range should the difference in sample means vary about 95% of the time in repeated independent samples of 100 measurements each from the two populations? e. What, in general, can be said about the variability of the difference between independent sample means relative to the variability of the individual sample means?

Problem 2E Independent random samples of 64 observations each are chosen from two normal populations with the following means and standard deviations: Let and denote the two sample means. a. Give the mean and standard deviation of the sampling distribution of b. Give the mean and standard deviation of the sampling distribution of c. Suppose you were to calculate the difference between the sample means Find the mean and standard deviation of the sampling distribution of d. Will the statistic be normally distributed? Explain.

To use the t-statistic to test for a difference between the means of two populations, what assumptions must be made about the two populations? About the two samples?

Problem 3E In order to compare the means of two populations, independent random samples of 400 observations are selected from each population, with the following results: Sample 1 Sample 2 = 5,275 = 5,240 s1 = 150 s2 = 200 a. Use a 95% confidence interval to estimate the difference between the population means (µ1-µ2) Interpret the confidence interval. ________________ b. Test the null hypothesis H0: (µ1-µ2) = 0 versus the alternative hypothesis Ha: Ha: (µ1-µ2) ? 0 Give the p-value of the test, and interpret the result. c. Suppose the test in part b were conducted with the alternative hypothesis Ha: Ha: (µ1-µ2) > 0 How would your answer to part b change? ________________ d. Test the null hypothesis H0: (µ1-µ2) = 25versus the alternative Ha: Ha: (µ1-µ2) ? 25.Give the p-value, and interpret the result. Compare your answer with that obtained from the test conducted in part b. ________________ e. What assumptions are necessary to ensure the validity of the inferential procedures applied in parts a–d?

Two populations are described in each of the following cases. In which cases would it be appropriate to apply the small-sample t-test to investigate the difference between the population means? a. Population 1: Normal distribution with variance \(\sigma_{1}^{2}\). Population 2: Skewed to the right with variance \(\sigma_{2}^{2}=\sigma_{1}^{2}\). b. Population 1: Normal distribution with variance \(\sigma_{1}^{2}\). Population 2: Normal distribution with variance \(\sigma_{2}^{2}\ \neq\ \sigma_{1}^{2}\). c. Population 1: Skewed to the left with variance \(\sigma_{1}^{2}\). Population 2: Skewed to the left with variance \(\sigma_{2}^{2}=\sigma_{1}^{2}\). d. Population 1: Normal distribution with variance \(\sigma_{1}^{2}\). Population 2: Normal distribution with variance \(\sigma_{2}^{2}=\sigma_{1}^{2}\). e. Population 1: Uniform distribution with variance \(\sigma_{1}^{2}\). Population 2: Uniform distribution with variance \(\sigma_{2}^{2}=\sigma_{1}^{2}\).

Independent random samples from normal populations produced the results shown in the next table. a. Calculate the pooled estimate of \(\sigma^2\). b. Do the data provide sufficient evidence to indicate that \(\mu_2>\mu_1\)? Test using \(\alpha=.10\). c. Find a 90% confidence interval for \(\left(\mu_1-\mu_2\right)\). d. Which of the two inferential procedures, the test of hypothesis in part b or the confidence interval in part c, provides more information about \(\left(\mu_1-\mu_2\right)\)?

Independent random samples of \(n_1=233\ \text{and}\ n_2=312\) are selected from two populations and used to test the hypothesis \(H_0:(\mu_1-\mu_2)=0\) against the alternative \(H_a:(\mu_1-\ \mu_2)\ \neq\ 0\). a. The two-tailed p-value of the test is .1150. Interpret this result. b. If the alternative hypothesis had been \(H_a:(\mu_1-\mu_2)\ <\ 0\), how would the p-value change? Interpret the p-value for this one-tailed test.

Problem 8E Two independent random samples have been selected— 100 observations from population 1 and 100 from population 2. Sample means = 26.6 and = 15.5 were obtained. From previous experience with these populations, it is known that the variances are = 9 and = 16. a. Find s b. Sketch the approximate sampling distribution for assuming = 10. c. Locate the observed value of on the graph you drew in part b. Does it appear that this value contradicts the null hypothesis ? d. Use the z-table to determine the rejection region for the test of against Use e. Conduct the hypothesis test of part d and interpret your result. f. Construct a 95% confidence interval for Interpret the interval. g. Which inference provides more information about the value of —the test of hypothesis in part e or the confidence interval in part f?

Problem 6E Assume that Calculate the pooled estimator of s2 for each of the following cases: Note that the pooled estimate is a weighted average of the sample variances. To which of the variances does the pooled estimate fall nearer in each of the above cases?

Problem 11E Independent random samples selected from two normal populations produced the sample means and standard deviations shown below. a. Conduct the test H0: (µ1 - µ2) = 0 against Ha: (µ1 - µ2) ? 0. Interpret the results. b. Estimate (µ1 - µ2) using a 95% confidence interval.

Problem 10E Independent random samples from approximately normal populations produced the results shown below. a. Do the data provide sufficient evidence to conclude that (µ2 - µ1) > 10? Test using ? = .01. b. Construct a 98% confidence interval for (µ2 - µ1). Interpret your result.

Lobster trap placement. Refer to the Bulletin of Marine Science (April 2010) study of lobster trap placement, Exercise. Recall that the variable of interest was the average distance separating traps—called trap spacing—deployed by teams of fishermen fishing for the red spiny lobster in Baja California Sur, Mexico. The trap spacing measurements (in meters) for a sample of 7 teams from the Bahia Tortugas (BT) fishing cooperative are repeated in the table. In addition, trap spacing measurements for 8 teams from the Punta Abreojos (PA) fishing cooperative are listed. (All these data are saved in the TRAPSPACE file). For this problem, we are interested in comparing the mean trap spacing measurements of the two fishing cooperatives. Based on Shester, G. G. “Explaining catch variation among Baja California lobster fishers through spatial analysis of trap-placement decisions.” Bulletin of Marine Science, Vol. 86, No. 2, April 2010 ( Table ), pp. 479–498. a. Identify the target parameter for this study. b. Compute a point estimate of the target parameter. c. What is the problem with using the normal ( z ) statistic to find a confidence interval for the target parameter? d. Find a 90% confidence interval for the target parameter. e. Use the interval, part d, to make a statement about the difference in mean trap spacing measurements of the two fishing cooperatives. f. What conditions must be satisfied for the inference, part e, to be valid?

Problem 13E Last name and acquisition timing. The speed with which consumers decide to purchase a product was investigated in the Journal of Consumer Research (August 2011). The researchers theorized that consumers with last names that begin with letters later in the alphabet will tend to acquire items faster than those whose last names begin with letters earlier in the alphabet—called the last name effect. MBA students were offered up to four free tickets to attend a top-ranked women’s college basketball game for which there was a limited supply of tickets. The first letter of the last name of those who responded to an e-mail offer in time to receive the tickets was noted as well as the response time (measured in minutes). The researchers compared the response times for two groups of MBA students: (1) those with last names beginning with one of the first nine letters of the alphabet and (2) those with last names beginning with one of the last nine letters of the alphabet. Summary statistics for the two groups are provided in the table. a. Construct a 95% confidence interval for the difference between the true mean response times for MBA students in the two groups. b. Based on the interval, part a, which group has the shorter mean response time? Does this result support the researchers’ last name effect theory? Explain.

Problem 15E Children’s recall of TV ads. Marketing professors at Robert Morris and Kent State Universities examined children’s recall and recognition of television advertisements (Journal of Advertising, Spring 2006). Two groups of children were shown a 60-second commercial for Sunkist FunFruit Rock-n-Roll Shapes. One group (the A/V group) was shown the ad with both audio and video; the second group (the video only group) was shown only the video portion of the commercial. Following the viewing, the children were asked to recall 10 specific items from the ad. The number of the 10 items recalled correctly by each child is summarized in the table. The researchers theorized that “children who receive an audiovisual presentation will have the same level of mean recall of ad information as those who receive only the visual aspects of the ad.” a. Set up the appropriate null and alternative hypotheses to test the researchers’ theory. b. Find the value of the test statistic. c. Give the rejection region for ? = .10. d. Make the appropriate inference. What can you say about the researchers’ theory? e. The researchers reported the p-value of the test as p-value = .542. Interpret this result. f. What conditions are required for the inference to be valid?

Effectiveness of teaching software. Educational software— ranging from video-game-like programs played on Sony PlayStations to rigorous drilling exercises used on computers— has become very popular in school districts across the country. The U.S. Department of Education (DOE) recently conducted a national study of the effectiveness of educational software. In one phase of the study, a sample of 1,516 first-grade students in classrooms that used educational software was compared to a sample of 1,103 first-grade students in classrooms that did not use the technology. In its Report to Congress (March 2007), the DOE concluded that “[mean] test scores [of students on the SAT reading test] were not significantly higher in classrooms using reading . . . software products” than in classrooms that did not use educational software. a. Identify the parameter of interest to the DOE. b. Specify the null and alternative hypotheses for the test conducted by the DOE. c. The p-value for the test was reported as .62. Based on this value, do you agree with the conclusion of the DOE? Explain.

Problem 17E Buy-side vs. sell-side analysts’ earnings forecasts. Refer to the Financial Analysts Journal (Jul./Aug. 2008) study of financial analysts’ forecast earnings, Exercise 2.86 (p. 86). Recall that data were collected on 3,526 forecasts made by buy-side analysts and 58,562 forecasts made by sell-side analysts, and the relative absolute forecast error was determined for each. The mean and standard deviation of forecast errors for both types of analysts are given in the table. a. Construct a 95% confidence interval for the difference between the mean forecast error of buy-side analysts and the mean forecast error of sell-side analysts. b. Based on the interval, part a, which type of analysis has the greater mean forecast error? Explain. c. What assumptions about the underlying populations of forecast errors (if any) are necessary for the validity of the inference, part b?

Drug content assessment. Refer to Exercise 4.123 (p. 240) and the Analytical Chemistry (Dec. 15, 2009) study in which scientists used high-performance liquid chromatography to determine the amount of drug in a tablet. Twenty-five tablets were produced at each of two different, independent sites. Drug concentrations (measured as a percentage) for the tablets produced at the two sites are listed in the table below. The scientists want to know whether there is any difference between the mean drug concentration in tablets produced at Site 1 and the corresponding mean at Site 2. Use the accompanying Minitab printout to help the scientists draw a conclusion.

Problem 18E Homework assistance for accounting students. How much assistance should accounting professors provide students for completing homework? Is too much assistance counterproductive? These were some of the questions of interest in a Journal of Accounting Education (Vol. 25, 2007) article. A total of 75 junior-level accounting majors who were enrolled in Intermediate Financial Accounting participated in an experiment. All students took a pretest on a topic not covered in class; then each was given a homework problem to solve on the same topic. However, the students were randomly assigned different levels of assistance on the homework. Some (20 students) were given the completed solution, some (25 students) were given check figures at various steps of the solution, and the rest (30 students) were given no help. After finishing the homework, each student was given a posttest on the subject. One of the variables of interest to the researchers was the knowledge gain (or, test score improvement), measured as the difference between the posttest and pretest scores. The sample mean knowledge gains for the three groups of students are provided in the table. a. The researchers theorized that as the level of homework assistance increased, the test score improvement from pretest to posttest would decrease. Do the sample means reported in the table support this theory? b. What is the problem with using only the sample means to make inferences about the population mean knowledge gains for the three groups of students? c. The researchers conducted a statistical test of hypothesis to compare the mean knowledge gain of students in the “no solutions” group to the mean knowledge gain of students in the “check figures” group. Based on the theory, part a, set up the null and alternative hypotheses for the test. d. The observed significance level of the t-test of part c was reported as .8248. Using ? = .05, interpret this result. e. The researchers conducted a statistical test of hypothesis to compare the mean knowledge gain of students in the “completed solutions” group to the mean knowledge gain of students in the “check figures” group. Based on the theory, part a, set up the null and alternative hypotheses for the test. f. The observed significance level of the t-test of part e was reported as .1849. Using ? = .05, interpret this result. g. The researchers conducted a statistical test of hypothesis to compare the mean knowledge gain of students in the “no solutions” group to the mean knowledge gain of students in the “completed solutions” group. Based on the theory, part a, set up the null and alternative hypotheses for the test. h. The observed significance level of the t-test of part g was reported as .2726. Using ? = .05, interpret this result.

Patent infringement case. Chance (Fall 2002) described a lawsuit charging Intel Corp. with infringing on a patent for an invention used in the automatic manufacture of computer chips. In response, Intel accused the inventor of adding material to his patent notebook after the patent was witnessed and granted. The case rested on whether a patent witness’s signature was written on top of or under key text in the notebook. Intel hired a physicist who used an X-ray beam to measure the relative concentrations of certain elements (e.g., nickel, zinc, potassium) at several spots on the notebook page. The zinc measurements for three notebook locations—on a text line, on a witness line, and on the intersection of the witness and text line—are provided in the following table and saved in the PATENT file. a. Use a test or a confidence interval (at \(\alpha\ =\ .05\) ) to compare the mean zinc measurement for the text line with the mean for the intersection. b. Use a test or a confidence interval (at \(\alpha\ =\ .05\) ) to compare the mean zinc measurement for the witness line with the mean for the intersection. c. From the results you obtained in parts a and b, what can you infer about the mean zinc measurements at the three notebook locations? d. What assumptions are required for the inferences to be valid? Are they reasonably satisfied?

Producer willingness to supply biomass. The conversion of biomass to energy is critical for producing transportation fuels. How willing are producers to supply biomass products such as cereal straw, corn stover, and surplus hay? To answer this question, economists conducted a survey of producers in both mid-Missouri and southern Illinois (Biomass and Energy, Vol. 36, 2012). Independent samples of 431 Missouri producers and 508 Illinois producers participated in the survey. Each producer was asked to give the maximum proportion of hay produced that he or she would be willing to sell to the biomass market. Summary statistics for the two groups of producers are listed in the table. Does the mean amount of surplus that hay producers are willing to sell to the biomass market differ for the two areas, Missouri and Illinois? Use \(\alpha\ =\ .05\) to make the comparison.

Problem 22E Service without a smile. “Service with a smile” is a slogan that many businesses adhere to. However, there are some jobs (e.g., those of judges, law enforcement officers, pollsters) that require neutrality when dealing with the public. An organization will typically provide “display rules” to guide employees on what emotions they should use when interacting with the public. A Journal of Applied Psychology (Vol. 96, 2011) study compared the results of surveys conducted using two different types of display rules: positive (requiring a strong display of positive emotions) and neutral (maintaining neutral emotions at all times). In this designed experiment, 145 undergraduate students were randomly assigned to either a positive display rule condition (n1 = 78) or a neutral display rule condition (n2 = 67). Each participant was trained on how to conduct the survey using the display rules. As a manipulation check, the researchers asked each participant to rate, on a scale of 1 = “strongly agree” to 5 = “strongly disagree,” the statement, “This task requires me to be neutral in my expressions.” a. If the manipulation of the participants was successful, which group should have the larger mean response? Explain. b. The data for the study (simulated based on information provided in the journal article) are listed in the table below. Access the data and run an analysis to determine if the manipulation was successful. Conduct a test of hypothesis using ? = .05. c. What assumptions, if any, are required for the inference from the test to be valid?

A paired difference experiment produced the following results: a. Determine the values of z for which the null hypothesis, µ1 - µ2 = 0, would be rejected in favor of the alternative hypothesis, µ1 - µ2 < 0. Use ? = .10. b. Conduct the paired difference test described in part a. Draw the appropriate conclusions. c. What assumptions are necessary so that the paired difference test will be valid? d. Find a 90% confidence interval for the mean difference md. e. Which of the two inferential procedures, the confidence interval of part d or the test of hypothesis of part b, provides more information about the differences between the population means?

Does rudeness really matter in the workplace? Studies have established that rudeness in the work- place can lead to retaliatory and counterproductive behavior. However, there has been little research on how rude behaviors in?uence a victim’s task performance. Such a study was conducted and the results published in the Academy of Management Journal (October 2007). College students enrolled in a management course were randomly assigned to one of two experimental conditions: rudeness condition (45 students) and control group (53 stu- dents). Each student was asked to write down as many uses for a brick as possible in 5 minutes. For those students in the rudeness condition, the facilitator displayed rudeness by berating the students in general for being irresponsible and unprofessional (due to a late-arriving confederate). No comments were made about the late-arriving confederate for students in the control group. The number of different uses for a brick was recorded for each of the 98 students and the data saved in the RUDE ?le, shown below. Conduct a statistical analysis (at ???? =.01) to determine if the true mean performance level for students in the rudeness condition is lower than the true mean performance level for students in the control group. Use the results shown on the accompanying SAS point out to draw your conclusion.

Problem 23E Is honey a cough remedy? Refer to the Archives of Pediatrics and Adolescent Medicine (Dec. 2007) study of honey as a children’s cough remedy, Exercise 2.30 (p. 61). Children who were ill with an upper respiratory tract infection and their parents participated in the study. Parents were instructed to give their sick child a dosage of liquid “medicine” prior to bedtime. Unknown to the parents, some were given a dosage of dextromethorphan (DM)—an over-the-counter cough medicine—while others were given a similar dose of honey. (Note: A third group gave their children no medicine.) Parents then rated their children’s cough symptoms, and the improvement in total cough symptoms score was determined for each child. The data (improvement scores) for the 35 children in the DM dosage group and the 35 children in the honey dosage group are reproduced in the table below. Do you agree with the statement (extracted from the article), “Honey may be a preferable treatment for the cough and sleep difficulty associated with childhood upper respiratory tract infection”? Use the comparison of two means methodology presented in this section to answer the question.

Problem 25E Ages of self-employed immigrants. Is self-employment for immigrant workers a faster route to economic advancement in the country? This was one of the questions studied in research published in the International Journal of Manpower (Vol. 32, 2011). One aspect of the study involved comparing the ages of self-employed and wage-earning immigrants. The researcher found that in Sweden, native wage earners tend to be younger than selfemployed natives. However, immigrant wage earners tend to be older than self-employed immigrants. This inference was based on summary statistics for male Swedish immigrants shown in the table. a. Based on the information given, why is it impossible to provide a measure of reliability for the inference “Selfemployed immigrants are younger, on average, than wage-earning immigrants in Sweden”? b. What information do you need to obtain a measure of reliability for the inference, part a? c. Give a value of the test statistic that would lead you to conclude that the true mean age of self-employed immigrants is less than the true mean age of wage-earning immigrants if you are willing to risk a Type I error rate of .01. d. Assume that s, the standard deviation of the ages, is the same for both self-employed and wage-earning immigrants. Give an estimate of s that would lead you to conclude that the true mean age of self-employed immigrants is less than the true mean age of wage-earning immigrants using ? = .01. e. Is the true value of s likely to be larger or smaller than the one you calculated in part d?

Cooling method for gas turbines. Refer to the Journal of Engineering for Gas Turbines and Power (Jan. 2005) study of gas turbines augmented with high-pressure inlet fogging, Exercise 7.40 (p. 378). The researchers classified gas turbines into three categories: traditional, advanced, and aeroderivative. Summary statistics on heat rate (kilojoules per kilowatt per hour) for each of the three types of gas turbines are shown in the Minitab printout (at the top of the next column). a. Is there sufficient evidence of a difference between the mean heat rates of traditional augmented gas turbines and aeroderivative augmented gas turbines? Test using \(\alpha\ =\ .05\). b. Is there sufficient evidence of a difference between the mean heat rates of advanced augmented gas turbines and aeroderivative augmented gas turbines? Test using \(\alpha\ =\ .05\).

Problem 27E A paired difference experiment yielded nd pairs of observations. In each case, what is the rejection region for testing H0 : µd > 2? a. n d = 12, ? = .05 b. n d = 24, ? = .10 c. n d = 4, ? = .025 d. n d = 80, ? = .01

Problem 28E T he data for a random sample of six paired observations are shown in the following table and saved in the LM7_33 file Pair Sample from Population 1 Sample from Population 2 1 7 4 2 3 1 3 9 7 4 6 2 5 4 4 6 8 7 a. Calculate the difference between each pair of observations by subtracting observation 2 from observation 1. Use the differences to calculate ________________ b. If ?1 and ? 2 are the means of populations 1 and 2, respectively, express md in terms of ? 1 and ? 2. ________________ c. Form a 95% confidence interval for ? d. ________________ d. Test the null hypothesis H0: ? d = 0 against the alternative hypothesis Ha: ?d ? 0 Use a = .05

Problem 31E Summer weight-loss camp. Camp Jump Start is an 8-week summer camp for overweight and obese adolescents. Counselors develop a weight-management program for each camper that centers on nutrition education and physical activity. In a study published in Pediatrics (April 2010), the body mass index (BMI) was measured for each of 76 campers both at the start and end of camp. Summary statistics on BMI measurements are shown in the table. Mean Standard Deviation Starting BMI Ending BMI Paired Differences 34.9 31.6 3.3 6.9 6.2 1.5 a. Give the null and alternative hypothesis for determining whether the mean BMI at the end of camp is less than the mean BMI at the start of camp. ________________ b. How should the data be analyzed, as an independent- samples t -test or as a paired-difference t -test? Explain. ________________ c. Calculate the test statistic using the formula for an independent-samples t-test. ( Note : This is not how the test should be conducted.) ________________ d. Calculate the test statistic using the formula for a paired-difference t -test. ________________ e. Compare the test statistics, parts c and d . Which test statistic provides more evidence in support of the alternative hypothesis? ________________ f. The p -value of the test, part d , was reported as p<6 .0001. Interpret this result assuming ? = .01 . ________________ g. Do the differences in BMI values need to be normally distributed in order for the inference, part f , to be valid? Explain. ________________ h. Find a 99% confidence interval for the true mean change in BMI for Camp Jump Start campers. Interpret the result.

The data for a random sample of 10 paired observations are shown in the table below. a. If you wish to test whether these data are sufficient to indicate that the mean for population 2 is larger than that for population 1, what are the appropriate null and alternative hypotheses? Define any symbols you use. b. Conduct the test, part a, using \(\alpha=.10\). c. Find a 90% confidence interval for \(\mu_d\). Interpret this result. d. What assumptions are necessary to ensure the validity of this analysis?

Problem 30E A paired difference experiment yielded the following results: n d = 40 ?d = 468 ?d2 = 6,880 a. Test H0 : µd = 10 against Ha : µd ? 10, where µd = (µ1 - µ2). Use ? = .05. b. Report the p-value for the test you conducted in part a. Interpret the p-value. c. Do you need to assume that the population of differences is normally distributed? Explain.

Problem 32E Performance ratings of government agencies. The U.S. Office of Management and Budget (OMB) requires government agencies to produce annual performance and accounting reports (PARS) each year. A research team at George Mason University evaluated the quality of the PARS for 24 government agencies (The Public Manager, Summer 2008), where evaluation scores ranged from 12 (lowest) to 60 (highest). The accompanying file contains evaluation scores for all 24 agencies for two consecutive years. (See Exercise 2.129, p. 105.) Data for a random sample of five of these agencies are shown in the accompanying table. Suppose you want to conduct a paired difference test to determine whether the true mean evaluation score of government agencies in year 2 exceeds the true mean evaluation score in year 1. a. Explain why the data should be analyzed using a paired difference test. b. Compute the difference between the year 2 score and the year 1 score for each sampled agency. c. Find the mean and standard deviation of the differences, part b. d. Use the summary statistics, part c, to find the test statistic. e. Give the rejection region for the test using ? = .10. f. Make the appropriate conclusion in the words of the problem.

Problem 33E Twinned drill holes. A traditional method of verifying mineralization grades in mining is to drill twinned holes, i.e., the drilling of a new hole, or “twin,” next to an earlier drill hole. The use of twinned drill holes was investigated in Exploration and Mining Geology (Vol. 18, 2009). Geologists use data collected at both holes to estimate the total amount of heavy minerals (THM) present at the drilling site. The data in the table on the next page (based on information provided in the journal article) represent THM percentages for a sample of 15 twinned holes drilled at a diamond mine in Africa. The geologists want to know if there is any evidence of a difference in the true THM means of all original holes and their twin holes drilled at the mine. a. Explain why the data should be analyzed as paired differences. b. Compute the difference between the “1st Hole” and “2nd Hole” measurements for each drilling location. c. Find the mean and standard deviation of the differences, part b. d. Use the summary statistics, part c, to find a 90% confidence interval for the true mean difference (“1st Hole” minus “2nd Hole”) in THM measurements. e. Interpret the interval, part d. Can the geologists conclude that there is no evidence of a difference in the true THM means of all original holes and their twin holes drilled at the mine?

NHTSA new car crash tests. Refer to the National Highway Traffic Safety Administration (NHTSA) crash test data on new cars, saved in the CRASH file. Crash test dummies were placed in the driver’s seat and front passenger’s seat of a new car model, and the car was steered by remote control into a head-on collision with a fixed barrier while traveling at 35 miles per hour. Two of the variables measured for each of the 98 new cars in the data set are (1) the severity of the driver’s chest injury and (2) the severity of the passenger’s chest injury. (The more points assigned to the chest injury rating, the more severe the injury is.) Suppose the NHTSA wants to determine whether the true mean driver chest injury rating exceeds the true mean passenger chest injury rating and, if so, by how much. a. State the parameter of interest to the NHTSA. b. Explain why the data should be analyzed as matched pairs. c. Find a 99% confidence interval for the true difference between the mean chest injury ratings of drivers and front-seat passengers. d. Interpret the interval you found in part c. Does the true mean driver chest injury rating exceed the true mean passenger chest injury rating? If so, by how much? e. What conditions are required for the analysis to be valid? Do these conditions hold for these data?

“I am not selling anything” surveys. To improve response rates in telephone surveys, interviewers are often instructed by the polling company to state, “I am not selling anything” at the outset of the call. The effectiveness of the “I am not selling anything” strategy was investigated in the International Journal of Public Opinion Research (Winter 2004). The sample consisted of 29 different telephone surveys. However, in each survey about half the people were contacted by interviewers using the “I am not selling anything” introduction and the other half were contacted by interviewers using the standard (no mention of “not selling”) introduction. Thus, for each of the 29 surveys, both the “not selling” and standard interviewing techniques were employed. Summary statistics on response rates (proportion of people called who actually responded to the survey questions) are given in the accompanying table. The goal of the researchers was to compare the mean response rates of the two interviewing methods with the specific purpose to determine if the mean response rate for “not selling” was higher than that for the standard. a. Explain why the data should be analyzed as a paired difference experiment. b. Analyse the data in the table using the independent samples t-test. Do you detect a significant difference between the mean response rates of the two methods using ? = .05? c. The researchers applied the paired difference t procedure and obtained an observed significance level of p-value = .001. Interpret this result if ? = 0.5. d. Compare the inferences you made in parts b and c.

Packaging of a children's health food. Refer to the Journal of Consumer Behaviour (Vol. 10,2011) study of packaging of a children's health food product, Exercise 7.33 (p. 376). Recall that a fictitious brand of a healthy food product sliced apples -was packaged to appeal to children (a smiling cartoon apple was on the front of the package). The researchers compared the appeal of this fictitious brand to the appeal of a commercially available brand of sliced apples, which was not packaged for children. Each of 408 schoolchildren rated both brands on a 5-point "willingness to eat" scale, with 1 = "not willing at all" and 5 = "very willing." The fictitious brand had a sample mean score of 3.69, while the commercially available brand had a sample mean score of 3.00. The researchers wanted to compare the population mean score for the fictitious brand, \(\mu_{\mathrm{F}}\), to the population, mean score for the commercially available brand, \(\mu_{\mathrm{C}}\). They theorized that \(\mu_{\mathrm{F}}\) would be greater than \(\mu_{\mathrm{C}}\). a. Specify the null and alternative hypotheses for the test. b. Explain how the researchers should analyze the data and why. c. The researchers reported a test statistic value of 5.71. Interpret this result. Use \(\alpha=.05\) to make your conclusion. d. Find the approximate p-value of the test. e. Could the researchers have tested at \(\alpha=.01\) and arrived at the same conclusion? Text Transcription: mu_F mu_C alpha = .05 alpha = .01

Problem 38E Acidity of mouthwash. Acid has been found to be a primary cause of dental caries (cavities). It is theorized that oral mouthwashes contribute to the development of caries due to the antiseptic agent oxidizing into acid over time. This theory was tested in the Journal of Dentistry, Oral Medicine and Dental Education (Vol. 3, 2009). Three bottles of mouthwash, each of a different brand, were randomly selected from a drugstore. The pH level (where lower pH levels indicate higher acidity) of each bottle was measured on the date of purchase and after 30 days. The data, saved in the MOUTHWASH file, are shown in the table. Conduct an analysis to determine if the mean initial pH level of mouthwash differs significantly from the mean pH level after 30 days. Use ? = .05 as your level of significance. Mouthwash Brand Initial pH Final pH LMW SMW RMW 4.56 6.71 5.65 4.27 6.51 5.58

Problem 37E Taking “power naps” during work breaks. Lack of sleep costs companies about $18 billion a year in lost productivity, according to the National Sleep Foundation. Companies are waking up to the problem, however. Some even have quiet rooms available for study or sleep. “Power naps” are in vogue (Athens Daily News, Jan. 9, 2000). A major airline recently began encouraging reservation agents to nap during their breaks. The accompanying table lists the number of complaints received about each of a sample of 10 reservation agents during the 6 months before naps were encouraged and during the 6 months after the policy change. a. Do the data present sufficient evidence to conclude that the new napping policy reduced the mean number of customer complaints about reservation agents? Test using ? = .05. b. What assumptions must hold to ensure the validity of the test? c. What variables, not controlled in the study, could lead to an invalid conclusion?

Problem 39E Testing electronic circuits. Japanese researchers have developed a compression/depression method of testing electronic circuits based on Huffman coding (IEICE Transactions on Information & Systems, Jan. 2005). The new method is designed to reduce the time required for input decompression and output compression—called the compression ratio. Experimental results were obtained by testing a sample of 11 benchmark circuits (all of different sizes) from a SUN Blade 1000 workstation. Each circuit was tested using the standard compression/depression method and the new Huffman-based coding method, and the compression ratio was recorded. The data are given in the accompanying table. Compare the two methods with a 95% confidence interval. Which method has the smaller mean compression ratio?

Problem 40E Impact of red light cameras on car crashes. To combat red-light-running crashes—the phenomenon of a motorist entering an intersection after the traffic signal turns red and causing a crash—many states are adopting photored enforcement programs. In these programs, red light cameras installed at dangerous intersections photograph the license plates of vehicles that run the red light. How effective are photo-red enforcement programs in reducing red-light-running crash incidents at intersections? The Virginia Department of Transportation (VDOT) conducted a comprehensive study of its newly adopted photored enforcement program and published the results in aJune 2007 report. In one portion of the study, the VDOT provided crash data both before and after installation of red light cameras at several intersections. The data (measured as the number of crashes caused by red light running per intersection per year) for 13 intersections in Fairfax County, Virginia, are given in the table and saved in the REDLIGHT file. Intersection Before Camera After Camera 1 2 3 4 5 6 7 8 9 10 11 12 13 3.60 0.27 0.29 4.55 2.60 2.29 2.40 0.73 3.15 3.21 0.88 1.35 7.35 1.36 0 0 1.79 2.04 3.14 2.72 0.24 1.57 0.43 0.28 1.09 4.92 Analyze the data for the VDOT. What do you conclude? Based on Virginia Transportation Research Council, “Research report: The impact of red light cameras (photo-red enforcement) on crashes in Virginia.” June 2007.

Problem 41E Evaluating a new drug. Merck Research Labs conducted an experiment to evaluate the effect of a new drug using the single-T swim maze. Nineteen impregnated dam rats were captured and allocated a dosage of 12.5 milligrams of the drug. One male and one female rat pup were randomly selected from each resulting litter to perform in the swim maze. Each pup was placed in the water at one end of the maze and allowed to swim until it escaped at the opposite end. If the pup failed to escape after a certain period of time, it was placed at the beginning of the maze and given another chance. The experiment was repeated until each pup accomplished three successful escapes. The table below reports the number of swims required by each pup to perform three successful escapes. Is there sufficient evidence of a difference between the mean number of swims required by male and female pups? Conduct the test (at ? = .10). Comment on the assumptions required for the test to be valid.

Problem 43E Consider making an inference about p1 - p2, where there are x1 successes in n1 binomial trials and x2 successes in n2 binomial trials. a. Describe the distributions of x1 and x2. b. Explain why the Central Limit Theorem is important in finding an approximate distribution for

Problem 42E Alcoholic fermentation in wines. Determining alcoholic fermentation in wine is critical to the wine-making process. Must/wine density is a good indicator of the fermentation point, since the density value decreases as sugars are converted into alcohol. For decades, winemakers have measured must/wine density with a hydrometer. Although accurate, the hydrometer employs a manual process that is very time consuming. Consequently, large wineries are searching for more rapid measures of density measurement. An alternative method utilizes the hydrostatic balance instrument (similar to the hydrometer, but digital). A winery in Portugal collected must/wine density measurements on white wine samples randomly selected from the fermentation process for a recent harvest. For each sample, the density of the wine at 20°C was measured with both the hydrometer and the hydrostatic balance. The densities for 40 wine samples are saved in the WINE40 file. The first five and last five observations are shown in the accompanying table. The winery will use the alternative method of mea-suring wine density only if it can be demonstrated that the mean difference between the density measurements of the two methods does not exceed .002. Perform the analysis for the winery. Provide the winery with a written report of your conclusions. Sample Hydrometer Hydrostatic 1 2 3 4 5 . . 36 37 38 39 40 1.08655 1.00270 1.01393 1.09467 1.10263 . . 1.08084 1.09452 0.99479 1.00968 1.00684 1.09103 1.00272 1.01274 1.09634 1.10518 . . 1.08097 1.09431 0.99498 1.01063 1.00526 Based on Cooperative Cellar of Borba (Adega Cooperativ a de Borba), Portugal.

Problem 45E In each case, determine whether the sample sizes are large enough to conclude that the sampling distribution of is approximately normal. a. n 1 = 12, n2 = 14, = .42, = .57 b. n 1 = 12, n2 = 14, = .92, = .86 c. n 1 = n2 = 30, = .70, = .73 d. n 1 = 100, n2 = 250, = .93, = .97 e. n 1 = 125, n2 = 200, = .08, = .12

Problem 44E For each of the following values of ?, find the values of z for which H0 : (p1 - p2) = 0 would be rejected in favor of Ha : (p1 - p2) < 0. a. ? = .01 : b. ? = .025 c. ? = .05 : d. ? = .10

Problem 47E Independent random samples, each containing 800 observations, were selected from two binomial populations. The samples from populations 1 and 2 produced 320 and 400 successes, respectively. a. Test H0 : (p1 - p2) = 0 against Ha : (p1 - p2) 7 0. Use a = .05. b. Test H0 : (p1 - p2) = 0 against Ha : (p1 - p2) ? 0. Use a = .01. c. Test H0 : (p1 - p2) = 0 against Ha : (p1 - p2) 6 0. Use a = .01. d. Form a 90% confidence interval for (p1 - p2).

Problem 48E Random samples of size n1 = 55 and n2 = 65 were drawn from populations 1 and 2, respectively. The samples yielded = .7 and = .6. Test H0 : (p1 - p2) = 0 against Ha : (p1 - p2) > 0 using ? = .05.

The “winner’s curse” in auction bidding. In auction bidding, the “winner’s curse” is the phenomenon of the winning (or highest) bid price being above the expected value of the item being auctioned. The Review of Economics and Statistics (Aug. 2001) published a study on whether bid experience impacts the likelihood of the winner’s curse occurring. Two groups of bidders in a sealed-bid auction were compared: (1) super-experienced bidders and (2) less-experienced bidders. In the super-experienced group, 29 of 189 winning bids were above the item’s expected value; in the less-experienced group, 32 of 149 winning bids were above the item’s expected value. a. Find an estimate of \(p_1\), the true proportion of super experienced bidders who fell prey to the winner’s curse. b. Find an estimate of \(p_2\), the true proportion of less experienced bidders who fell prey to the winner’s curse. c. Construct a 90% confidence interval for \(p_1 - p_2\). d. Give a practical interpretation of the confidence interval, part c. Make a statement about whether bid experience impacts the likelihood of the winner’s curse occurring.

Problem 46E Construct a 95% confidence interval for (p1 - p2) in each of the following situations: a. n1 = 400, p?1 = .65; n2 = 400, p?2 = .58 ________________ b. n1 = 180, p?1 = .31; n2 = 250, p?2 = .25 ________________ c. n1 = 100, p?1 = .46; n2 = 120, p?2 = .61

Is steak your favorite barbeque food? July is National Grilling Month in the United States. On July 1, 2008, The Harris Poll #70 reported on a survey of Americans’ grilling preferences. When asked about their favorite food prepared on a barbeque grill, 662 of 1,250 randomly sampled Democrats preferred steak, as compared to 586 of 930 randomly sampled Republicans. a. Give a point estimate for the proportion of all Democrats who prefer steak as their favorite barbeque food. b. Give a point estimate for the proportion of all Republicans who prefer steak as their favorite barbeque food. c. Give a point estimate for the difference between the proportions of all Democrats and all Republicans who prefer steak as their favorite barbeque food. d. Construct a 95% confidence interval for the difference between the proportions of all Democrats and all Republicans who prefer steak as their favorite barbeque food. e. Give a practical interpretation of the interval, part d. f. Explain the meaning of the phrase “95% confident” in your answer to part e.

Problem 52E Planning-habits survey. American Demographics (Jan. 2002) reported the results of a survey on the planning habits of men and women. In response to the question “What is your preferred method of planning and keeping track of meetings appointments, and deadlines?” 56% of the men and 46% of the women answered “I keep them in my head.” A nationally representative sample of 1,000 adults participated in the survey; therefore, assume that 500 were men and 500 were women. a. Set up the null and alternative hypotheses for testing whether the percentage of men who prefer keeping track of appointments in their head is larger than the corresponding percentage of women. ________________ b. Compute the test statistic for the test. ________________ c. Give the rejection region for the test, using ? = .01. ________________ d. Find the p -value for the test. ________________ e. Draw the appropriate conclusion.

Electronic vs. printed surveys. The rapid evolution of computer hardware and software has made it easy for businesses to conduct computer-based and Web-based (i.e., electronic) surveys. Professors at Michigan State and DePaul Universities collaborated on a study designed to compare the response rates of electronic surveys and traditional print surveys (Decision Sciences Institute, Decision Line, July 2001). The two surveys were developed for customers who had purchased products over the Internet from a leading retailer of office supplies. Of the 631 customers mailed the printed survey, 261 returned usable responses. Of the 414 customers who were sent a computer disk with the electronic survey, 155 returned usable responses. a. Estimate the difference between the response rates of the two survey types using a 90% confidence interval. Interpret the result. b. If the difference in response rates is 5% or less, the researchers will infer that there is no “practical” difference in response rates for the two surveys. Are the researchers able to make this inference? Explain.

Hospital administration of malaria patients. One of the most serious health problems in India is malaria. Consequently, Indian hospital administrators must have the resources to treat the high volume of malaria patients that are admitted. Research published in the National Journal ofCommunity Medicine (Vol. 1, 2010) investigated whether the malaria admission rate is higher in some months than in others. In a sample of 192 hospital patients admitted in January, 32 were treated for malaria. In an independent sample of 403 patients admitted in May (4 months later), 34were treated for malaria. a. Describe the two populations of interest in this study. b. Give a point estimate of the difference in the malaria admission rates in January and May. c. Find a 90% confidence interval for the difference in the malaria admission rates in January and May. d. Based on the interval, part c, can you conclude that a difference exists in the true malaria admission rates in January and May? Explain.

Producer willingness to supply biomass. Refer to the Biomass and Energy (Vol. 36, 2012) study of the willingness of producers to supply biomass products such as surplus hay, Exercise 8.20 (p. 436). Recall that independent samples of Missouri producers and Illinois producers were surveyed. Another aspect of the study focused on the services producers were willing to supply. One key service involves windrowing (mowing and piling) of hay. Of the 558 Missouri producers surveyed, 187 were willing to offer windrowing services; of the 940 Illinois producers surveyed, 380 were willing to offer windrowing services. The researchers want to know if the proportion of producers who were willing to offer windrowing services to the biomass market differs for the two areas, Missouri and Illinois. a. Specify the parameter of interest to the researchers. b. Set up the null and alternative hypotheses for testing whether the proportion of producers who were willing to offer windrowing services differs in Missouri and Illinois. c. A Minitab analysis of the data is shown below. Locate the test statistic on the printout. d. Give the rejection region for the test using \(\alpha\ =\ .01\). e. Locate the p-value of the test on the printout. f. Make the appropriate conclusion using both the p-value and rejection region approach. Your conclusions should agree.

Salmonella in produce. Salmonella is the most common type of bacterial food-borne illness in the United States. How prevalent is salmonella in produce grown in the major agricultural region of Monterey, California? Researchers from the U.S. Department of Agriculture (USDA) conducted tests for salmonella in produce grown in the region and published their results in Applied and Environmental Microbiology (April 2011). In a sample of 252 cultures obtained from water used to irrigate the region, 18 tested positive for salmonella. In an independent sample of 476 cultures obtained from the region’s wildlife (e.g., birds), 20 tested positive for salmonella. Is this sufficient evidence for the USDA to state that the prevalence of salmonella in the region’s water differs from the prevalence of salmonella in the region’s wildlife? Use \(\alpha\ =\ .01\) to make your decision.

Problem 56E Angioplasty’s benefits challenged. Each year, more than 1 million heart patients undergo an angioplasty. The benefits of an angioplasty were challenged in a recent study of 2,287 patients (2007 Annual Conference of the American College of Cardiology, New Orleans). All the patients had substantial blockage of the arteries, but were medically stable. All were treated with medication such as aspirin and beta-blockers. However, half the patients were randomly assigned to get an angioplasty and half were not. After five years, the researchers found that 211 of the 1,145 patients in the angioplasty group had subsequent heart attacks, compared with 202 of 1,142 patients in the medicationonly group. Do you agree with the study’s conclusion that “There was no significant difference in the rate of heart attacks for the two groups”? Support your answer with a 95% confidence interval.

Entrepreneurial careers of MBA alumni. Are African American MBA students more likely to begin their careers as entrepreneurs than white MBA students? This was a question of interest to the Graduate Management Admission Council (GMAC). GMAC Research Reports (Oct. 3, 2005) published the results of a survey of MBA alumni. Of the 1,304 African Americans who responded to the survey, 209 reported their employment status after graduation as self-employed or a small business owner. Of the 7,120 whites who responded to the survey, 356 reported their employment status after graduation as self-employed or a small business owner. Use this information to answer the research question.

Problem 60E Religious symbolism in TV commercials. Gonzaga University professors conducted a study of television commercials and published their results in the Journal of Sociology, Social Work and Social Welfare (Vol. 2, 2008). The key research question was: “Do television advertisers use religious symbolism to sell goods and services?” In a sample of 797 TV commercials collected in 1998, only 16 commercials used religious symbolism. Of the sample of 1,499 TV commercials examined in the more recent study, 51 commercials used religious symbolism. Conduct an analysis to determine if the percentage of TV commercials that use religious symbolism has changed since the 1998 study. If you detect a change, estimate the magnitude of the difference and attach a measure of reliability to the estimate.

Problem 59E Food craving study. Do you have an insatiable craving for chocolate or some other food? Because many North Americans apparently do, psychologists are designing scientific studies to examine the phenomenon. According to the New York Times (Feb. 22, 1995), one of the largest studies of food cravings involved a survey of 1,000 McMaster University (Canada) students. The survey revealed that 97% of the women in the study acknowledged specific food cravings while only 67% of the men did. a. How large do n1 and n2 need to be to conclude that the true proportion of women who acknowledged having food cravings exceeds the corresponding proportion of men? Assume ? = .01. b. Why is it dangerous to conclude from the study that women have a higher incidence of food cravings than men?

Assuming that \(n_1 = n_2\), find the sample sizes needed to estimate (\(p_1 - p_2\)) for each of the following situations: a. Margin of error = .01 with 99% confidence. Assume that \(p_1\ \approx\ .4\) and \(p_2\ \approx\ .7\). b. A 90% confidence interval of width .05. Assume that there is no prior information available to obtain approximate values of \(p_1\) and \(p_2\). c. Margin of error = .03 with 90% confidence. Assume that \(p_1\ \approx\ .2\ \text{and}\ p_2\ \approx\ 3\).

Problem 62E Find the appropriate values of n1 and n2 (assume n1 = n2) needed to estimate (?1 - ?2) for each of the following situations: a. A margin of error equal to 3.2 with 95% confidence. From prior experience it is known that ?1 ? 15 and ?2 ?17. b. A margin of error equal to 8 with 99% confidence. The range of each population is 60. c. A 90% confidence interval of width 1.0. Assume that ?12 ? 5.8 and ?22 ? 7.5.

Problem 63E Suppose you want to estimate the difference between two population means correct to within 1.8 with a 95% confidence interval. If prior information suggests that the population variances are approximately equal to ?12 = ?2 2 = 14 and you want to select independent random samples of equal size from the populations, how large should the sample sizes, n1 and n2, be?

Problem 64E Enough money has been budgeted to collect independent random samples of size n1 = n2 = 100 from populations 1 and 2 to estimate (?1 - ?2). Prior information indicates that ?1 = ?2 = 10. Have sufficient funds been allocated to construct a 90% confidence interval for (?1 - ? 2) of width 5 or less? Justify your answer.

Problem 65E Last name and acquisition timing. Refer to the Journal of Consumer Research (August 2011) study of the last name effect in acquisition timing, Exercise 8.13 (p. 433). Recall that the mean response times (in minutes) to acquire basketball tickets were compared for two groups of MBA students-those students with last names beginning with one of the first nine letters of the alphabet and those with last names beginning with one of the last nine letters of the alphabet. How many MBA students from each group would need to be selected to estimate the difference in mean times to within 2 minutes of its true value with 95% confidence? (Assume equal sample sizes were selected for each group and that the response time standard deviation for both groups is ? ? 9 minutes.)

Problem 67E Electronic vs. printed surveys. Refer to the Decision Line (July 2001) study designed to compare the response rates of electronic surveys and traditional print surveys, Exercise 8.54 (p. 454). Recall that the two surveys were developed for customers who had purchased products over the Internet from a leading retailer of office supplies. How many customers should be sampled to estimate the difference between the response rates of the two survey types to within .01 using a 90% confidence interval? Assume the same number of customers should be sampled for each survey.

Homework assistance for accounting students. Refer to the Journal of Accounting Education (Vol. 25, 2007) study of providing homework assistance to accounting students, Exercise 8.18 (p. 435). Recall that one group of students was given a completed homework solution and another group was given only check figures at various steps of the solution. The researchers wanted to compare the average test score improvement of the two groups. How many students should be sampled in each group to estimate the difference in the averages to within .5 point with 99% confidence? Assume that the standard deviations of the test score improvements for the two groups are approximately equal to 1.

Problem 68E Conducting a political poll. A pollster wants to estimate the difference between the proportions of men and women who favor a particular national candidate using a 90% confidence interval of width .04. Suppose the pollster has no prior information about the proportions. If equal numbers of men and women are to be polled, how large should the sample sizes be?

Users of home shopping services. All cable companies carry at least one home shopping channel. Who uses these home shopping services? Are the shoppers primarily men or women? Suppose you want to estimate the difference in the proportions of men and women who say they have used or expect to use televised home shopping using an 80% confidence interval of width .06 or less. a. Approximately how many people should be included in your samples? b. Suppose you want to obtain individual estimates for the two proportions of interest. Will the sample size found in part a be large enough to provide estimates of each proportion correct to within .02 with probability equal to .90? Justify your response.

Problem 71E Angioplasty’s benefits challenged. Refer to the study of patients with substantial blockage of the arteries presented at the 2007 Annual Conference of the American College of Cardiology, Exercise 8.56 (p. 455). Recall that half the patients were randomly assigned to get an angioplasty and half were not. The researchers compared the proportion of patients with subsequent heart attacks for the two groups and reported no significant difference between the two proportions. Although the study involved over 2,000 patients, the sample size may have been too small to detect a difference in heart attack rates. a. How many patients must be sampled in each group to estimate the difference in heart attack rates to within .015 with 95% confidence? (Use summary data from Exercise 8.56 in your calculation.) b. Comment on the practicality of carrying out the study with the sample sizes determined in part a. c. Comment on the practical significance of the difference detected in the confidence interval for the study, part a.

Average housing space per person. Even though Japan is an economic superpower, Japanese workers are in many ways worse off than their U.S. and European counterparts. For example, the estimated average housing space per person (in square feet) is 645 in the United States but only 344 in Japan (Diawa House Industry, Co., Japan). Suppose a team of economists and sociologists from the United Nations plans to reestimate the difference in the mean housing space per person for U.S. and Japanese workers. Assume that equal sample sizes will be used for each country and that the standard deviation is 35 square feet for Japan and 80 for the United States. How many people should be sampled in each country to estimate the difference to within 10 square feet with 95% confidence?

Problem 69E Life expectancies of working women and housewives. Is housework hazardous to your health? A study in Public Health Reports compared the life expectancies of 25-yearold white women in the labor force to those who are housewives. How large a sample would have to be taken from each group in order to be 95% confident that the estimate of difference in average life expectancies for the two groups is within 1 year of the true difference in average life expectancies? Assume that equal sample sizes will be selected from the two groups and that the standard deviation for both groups is approximately 15 years.

Problem 73E Use Tables V, VI, VII, and VIII in Appendix D to find each of the following F-values: a. F .05 where v1 = 9 and v2 = 6 b. F .01 where v1 = 18 and v2 = 14 c. F.025 where v1 = 11 and v2 = 4 d. F.10 where v1 = 20 and v2 = 5

Problem 74E Given v1 and v2, find the following probabilities: a. v1 = 2, v2 = 30, b. v1 = 24, v2 = 10, c. v1 = 7, v2 = 1, d. v1 = 40, v2 = 40,

Problem 75E For each of the following cases, identify the rejection region that should be used to test against . Assume v1 = 30 and v2 = 20. a. ? = .10 : b. ? = .05 c. ? = .025 : d. ? = .01

For each of the following cases, identify the rejection region that should be used to test \(H_{0}: \sigma_{1}^{2}=\sigma_{2}^{2}\) against \(H_{\mathrm{a}}: \sigma_{1}^{2} \neq \sigma_{2}^{2}\). Assume \(\nu_{1}=10\) and \(\nu_{2}=12\). a. \(\alpha=.20\) b. \(\alpha=.10\) c. \(\alpha=.05\) d. \(\alpha=.02\) Text Transcription: H_{0}: sigma_{1}^{2} = sigma_{2}^{2} H_a: sigma_{1}^{2} neq sigma_{2}^{2} nu_{1} = 10 nu_{2} = 12 alpha = .20 alpha =.10 alpha = .05 alpha = .02

Problem 77E Specify the appropriate rejection region for testing in each of the following situations:

Problem 78E Independent random samples were selected from each of two normally distributed populations, n1 = 12 from population 1 and n2 = 27 from population 2. The means and variances for the two samples are shown in the table. a. Test the null hypothesis against the alternative hypothesis . Use ? = .10. b. Find and interpret the approximate p-value of the test.

Problem 79E Independent random samples were selected from each of two normally distributed populations, n1 = 6 from population1 and n2 = 5 from population 2. The data are shown in the table. a. Test against . Use ? = .01. b. Find and interpret the approximate p-value of the test.

Children’s recall of TV ads. Refer to the Journal of Advertising (Spring 2006) study of children’s recall of television commercials, Exercise 8.15 (p. 434). You used a smallsample t-test to test the null hypothesis \(H_0:(\mu_1-\mu_2)=0\), where \(\mu_1\) = mean number of ads recalled by children in the video only group and \(\mu_2\) = mean number of ads recalled by children in the A/V group. Summary statistics for the study are reproduced in the table below. The validity of the inference derived from the test is based on the assumption of equal group variances, i.e., \(\sigma_{1}^{2}=\sigma_{2}^{2}\). a. Set up the null and alternative hypotheses for testing this assumption. b. Compute the test statistic. c. Find the rejection region for the test using \(\alpha\ =\ .10\). d. Make the appropriate conclusion in the words of the problem. e. Comment on the validity of the inference derived about the difference in population means in Exercise 8.15.

Patent infringement case. ?Refer to the Chance (Fall 2002) description of a patent infringement case against Intel Corp., Exercise 8.19 (p. 435). The zinc measurements for three locations on the original inventor’s notebook— on a text line, on a witness line, and on the intersection of the witness and text line—are reproduced in the table. a. ?Use a test (at a = .05) to compare the variation in zinc measurements for the text line with the corresponding variation for the intersection. b. ?Use a test (at a = .05) to compare the variation in zinc measurements for the witness line with the corresponding variation for the intersection. c. ?From the results, parts a ?and b, ?what can you infer about the variation in zinc measurements at the three notebook locations? d. ?What assumptions are required for the inferences to be valid? Are they reasonably satisfied? (You checked these assumptions when answering Exercise 8.19d.)

Problem 82E 8.82 Mental health of workers and the unemployed. A study in the Journal of Occupational and Organizational Psychology investigated the relationship of employment status and mental health. A sample of working and unemployed people was selected, and each person was given a mental health examination using the General Health Questionnaire (GHQ), a widely recognized measure of mental health. Although the article focused on comparing the mean GHQ levels, a comparison of the variability of GHQ scores for employed and unemployed men and women is of interest as well. a. In general terms, what does the amount of variability in GHQ scores tell us about the group? b. What are the appropriate null and alternative hypotheses to compare the variability of the mental health scores of the employed and unemployed groups? Define any symbols you use. c. The standard deviation for a sample of 142 employed men was 3.26, while the standard deviation for 49 unemployed men was 5.10. Conduct the test you set up in part b using ? = .05. Interpret the results. d. What assumptions are necessary to ensure the validity of the test?

Problem 83E Drug content assessment. Refer to Exercise 8.16 (p. 434) and the Analytical Chemistry (Dec. 15, 2009) study in which scientists used high-performance liquid chromatography to determine the amount of drug in a tablet. Recall that 25 tablets were produced at each of two different, independent sites. The researchers want to determine if the two sites produced drug concentrations with different variances. A Minitab printout of the analysis follows. Locate the test statistic and p-value on the printout. Use these values and a = .05 to conduct the appropriate test for the researchers.

Lobster trap placement. Refer to the Bulletin of Marine Science (April 2010) study of lobster trap placement, Exercise 8.12 (p. 433). The data are repeated here (next column). You used the small-sample t-statistic to form a confidence interval for the difference between the mean trap-spacing measurements of the two fishing cooperatives. This method requires the variance of the population of trap spacings for the BT cooperative, \((\sigma_{BT})^2\) to be the same as the population variance for the PA cooperative, \((\sigma_{PA})^2\). a. Set up the null and alternative hypotheses for testing the equality of variances. b. Find the sample variances for the two cooperatives. c. Compute the test statistic. d. Find the approximate p-value of the test. e. Make the appropriate conclusion using \(\alpha\ =\ .01\).

Problem 85E Analyzing human inspection errors. Tests of product quality using human inspectors can lead to serious inspection error problems (Journal of Quality Technology). To evaluate the performance of inspectors in a new company, a quality manager had a sample of 12 novice inspectors evaluate 200 finished products. The same 200 items were evaluated by 12 experienced inspectors. The quality of each item—whether defective or nondefective—was known to the manager. The table lists the number of inspection errors (classifying a defective item as nondefective or vice versa) made by each inspector. a. Prior to conducting this experiment, the manager believed the variance in inspection errors was lower for experienced inspectors than for novice inspectors. Do the sample data support her belief? Test using ? = .05. b. What is the appropriate p-value of the test you conducted in part a?

Problem 86E Cooling method for gas turbines. Refer to the Journal of Engineering for Gas Turbines and Power (Jan. 2005) study of gas turbines augmented with high-pressure inlet fogging, Exercise 8.24 (p. 437). Heat rate data (kilojoules per kilowatt per hour) for each of three types of gas turbines (advanced, aeroderivative, traditional) are saved in the accompanying file. In order to compare the mean heat rates of two types of gas turbines, you assumed that the heat rate variances were equal. a. Conduct a test (at ? = .05) for equality of heat rate variances for traditional and aeroderivative augmented gas turbines. Use the result to make a statement about the validity of the inference derived in Exercise 8.24a. b. Conduct a test (at ? = .05) for equality of heat rate variances for advanced and aeroderivative augmented gas turbines. Use the result to make a statement about the validity of the inference derived in Exercise 8.24b.

Problem 89SE List the assumptions necessary for each of the following inferential techniques: a. Large-sample inferences about the difference (?1 - ?2) between population means using a two-sample z-statistic b. Small-sample inferences about (?1 - ?2) using an independent samples design and a two-sample t-statistic c. Small-sample inferences about (?1 - ?2) using a paired difference design and a single-sample t-statistic to analyze the differences d. Large-sample inferences about the differences (p1 - p2) between binomial proportions using a two sample z-statistic e. Inferences about the ratio of two population variances using an F-test.

Problem 87E “Just-in-time” deliveries from factories to foxholes. Following the initial Persian Gulf War, the Pentagon changed its logistics processes to be more corporate-like. The extravagant “just-in-case” mentality was replaced with “just-in-time” systems. Emulating FedEx and United Parcel Service, deliveries from factories to foxholes are now expedited using bar codes, laser cards, radio tags, and databases to track supplies. The table below contains order-to-delivery times (in days) for a sample of shipments from the United States to the Persian Gulf and a sample of shipments to Bosnia. a. Is there sufficient evidence to indicate that the variances in order-to-delivery times for Persian Gulf and Bosnia shipments differ? Use ? = .05. b. Given your answer to part a, is it appropriate to construct a confidence interval for the difference between the mean order-to-delivery times? Explain.

Is honey a cough remedy? Refer to the Archives of Pediatrics and Adolescent Medicine (Dec. 2007) study of honey as a children’s cough remedy, Exercise 8.23 (p. 437). The data (cough improvement scores) for the 33 children in the DM dosage group and the 35 children in the honey dosage group are reproduced in the table below. In Exercise 8.23, you used a comparison of two means to determine whether “honey may be a preferable treatment for the cough and sleep difficulty associated with childhood upper respiratory tract infection.” The researchers also want to know if the variability in coughing improvement scores differs for the two groups. Conduct the appropriate analysis, using \(\alpha\ =\ .10.3\).

Problem 91SE Independent random samples were selected from two normally distributed populations with means m1 and m2, respectively. The sample sizes, means, and variances are shown in the following table: a. Test H0: (?1 – ?2) = 0 against Ha: (?1 – ?2)> 0. Use ? = .05. ________________ b. Form a 99% confidence interval for (?1 – ?2). ________________ c. How large must n1 and n2 be if you wish to estimate (?1 – ?2)to within two units with 99% confidence? Assume that n1 = n2. Sample 1 Sample 2 n1 = 12 = 17.8 s21 = 74.2 n2 = 14 = 15.3 s22= 60.5

Problem 90SE Two independent random samples were selected from normally distributed populations with means and variances and , respectively. The sample sizes, means, and variances are shown in the following table. a. Test against . Use a = .05. b. Would you be willing to use a small sample t-test to test the null hypothesis against the alternative hypothesis Why?

Problem 92SE Independent random samples were selected from two binomial populations. The sizes and number of observed successes for each sample are shown in the following table. a. Test H0: ( p1 - p2) = 0 against Ha: ( p1 - p2) < 0. Use ? = .10. b. Form a 95% confidence interval for ( p1 - p2). c. What sample sizes would be required if we wish to use a 95% confidence interval of width .01 to estimate ( p1 - p2)?

Problem 93SE Two independent random samples are taken from two populations. The results of these samples are summarized in the following table: ________________ a. Form a 90% confidence interval for (?1 – ?2). ________________ b. Test H0: (?1 – ?2) = 0 against Use ? = .01. ________________ c. What sample size would be required if you wish to estimate (m1 - m2) to within .2 with 90% confidence? Assume that n1 = n2. Sample 1 Sample 2 n1 = 135 = 12.2 s21= 2.1 n2 = 148 = 8.3 s22= 3.0 V

Problem 94SE A random sample of nine pairs of observations is recorded on two variables x and y . The data are shown in the following table and saved in the LM7_119 file. Do the data provide sufficient evidence to indicate that the probability distribution for x is shifted to the right of that for y? Test, using ? = .05. Pair x y 1 2 3 4 5 6 7 8 9 19 27 15 35 13 29 16 22 16 12 19 7 25 11 10 16 10 18

Problem 95SE Determining the target parameter. For each of the following studies, give the parameter of interest and state any assumptions that are necessary for the inferences to be valid. a. To investigate a possible link between jet lag and memory impairment, a University of Bristol (England) neurologist recruited 20 female flight attendants who worked flights across several time zones. Half of the attendants had only a short recovery time between flights and half had a long recovery time between flights. The average size of the right temporal lobe of the brain for the short-recovery group was significantly smaller than the average size of the right temporal lobe of the brain for the long-recovery group (Tampa Tribune, May 23, 2001). b. In a study presented at the March 2001 meeting of the Association for the Advancement of Applied Sport Psychology, researchers revealed that the proportion of athletes who have a good self-image of their body is 20% higher than the corresponding proportion of nonathletes. c. A University of Florida animal sciences professor has discovered that feeding chickens corn oil causes them to produce larger eggs (UF News, April 11, 2001). The weight of eggs produced by each of a sample of chickens on a regular feed diet was recorded. Then, the same chickens were fed a diet supplemented by corn oil, and the weight of eggs produced by each was recorded. Themean weight of the eggs produced with corn oil was 3 grams heavier than the mean weight produced with the regular diet.

Problem 96SE Financial incentives for college students. A study reported in Inside Higher Education News (May 22, 2006) found that financial incentives can improve low-income college students’ grades and retention. As part of their “Opening Doors” program, a Louisiana community college offered to pay students $1,000 per semester on condition that they maintain at least half-time enrollment and at least a 2.0 grade point average (GPA). a. About 61% of Opening Doors students enrolled full time as opposed to about 52% of traditional students. Identify the target parameter for this comparison. b. The mean GPA of Opening Doors students was 2.3 as compared to the mean GPA of 2.1 for traditional students. Identify the target parameter for this comparison.

Problem 98SE Hull failures of oil tankers. Refer to the Marine Technology (Jan. 1995) study of major oil spills from tankers and carriers, Exercise 2.159 (p. 117). The data for the 42 recent spills are saved in the accompanying file. a. Construct a 90% confidence interval for the difference between the mean spillage amount of accidents caused by collision and the mean spillage amount of accidents caused by fire/explosion. Interpret the result. b. Conduct a test of hypothesis to compare the mean spillage amount of accidents caused by grounding to the corresponding mean of accidents caused by hull failure. Use ?= .05. c. Refer to parts a and b. State any assumptions required for the inferences derived from the analyses to be valid. Are these assumptions reasonably satisfied? d. Conduct a test of hypothesis to compare the variation in spillage amounts for accidents caused by collision and accidents caused by grounding. Use ? = .02.

Problem 100SE Durability of shock absorbers. A manufacturer of automobile shock absorbers was interested in comparing the durability of its shocks with that of the shocks produced by its biggest competitor. To make the comparison, one of the manufacturer’s and one of the competitor’s shocks were randomly selected and installed on the rear wheels of each of six cars. After the cars had been driven 20,000 miles, the strength of each test shock was measured, coded, and recorded. Results of the examination are shown in the table. a. Explain why the data are collected as matched pairs. b. Do the data present sufficient evidence to conclude that there is a difference in the mean strength of the two types of shocks after 20,000 miles of use? Use ? = .05. c. Find the approximate observed significance level for the test and interpret its value. d. What assumptions are necessary to apply a paired difference analysis to the data? e. Construct a 95% confidence interval for µd. Interpret the confidence interval. f. Suppose the data are based on independent random samples. Construct a 95% confidence interval for (µ1 - µ2). Interpret your result. g. Compare the confidence intervals you obtained in parts e and f. Which is wider? To what do you attribute the difference in width? Assuming in each case that the appropriate assumptions are satisfied, which interval provides you with more information about (µ1 - µ2)? Explain. h. Are the results of an unpaired analysis valid if the data come from a paired experiment?

Problem 97SE Rating service at five-star hotels. A study published in The Journal of American Academy of Business, Cambridge (March 2002) examined whether the perception of service quality at five-star hotels in Jamaica differed by gender. Hotel guests were randomly selected from the lobby and restaurant areas and asked to rate 10 service-related items (e.g., “The personal attention you received from our employees”). Each item was rated on a 5-point scale (1 = “much worse than I expected,” 5 = “much better than I expected”), and the sum of the items for each guest was determined. A summary of the guest scores is provided in the table. a. Construct a 90% confidence interval for the difference between the population mean service-rating scores given by male and female guests at Jamaican five-star hotels. b. Conduct a test to determine if the service-rating score variances differ by gender. Use ? = .10 c. Use the results, parts a and b, to make an inference about whether the perception of service quality at five-star hotels in Jamaica differs by gender.

Financial incentives for college students. Do students who play virtual-reality educational software games perform better in school? If so, software designers will use this information to create more attractive and motivating educational software. In a study published in Educational Technology & Society (April 2005), a class of 90 elementary schoolchildren were randomly divided into two groups of 45. One group used a virtual-reality game called VR-ENGAGE to learn about geography. The other group learned geography on the computer with a simple user interface. All students were given an exam at the beginning and the end of the learning period. The difference in test scores was used to find the percentage improvement in scores for each student. The following table summarizes the results for the two groups. a. Visually inspect the summary results. Does it appear that the mean improvement in scores for the virtual reality group is greater than the mean for the simple user interface group? b. Conduct an analysis (either a confidence interval or a test of hypothesis) at \(\alpha\ =\ .05\) to support your observation in part a.

Problem 101SE Life expectancy of Oscar winners. Does winning an Academy of Motion Picture Arts and Sciences award lead to long-term mortality for movie actors? In an article in the Annals of Internal Medicine (May 15, 2001), researchers sampled 762 Academy Award winners and matched each one with another actor of the same sex who was in the same winning film and was born in the same era. The life expectancies (ages) of the pairs of actors were compared. a. Explain why the data should be analyzed as a paired difference experiment. ________________ b. Set up the null hypothesis for a test to compare the mean life expectancies of Academy Award winners and nonwinners. ________________ c. The sample mean life expectancies of Academy Award winners and nonwinners were reported as 79.7 years and 75.8 years, respectively. The p -value for comparing the two population means was reported as p = .003. Interpret this value in the context of the problem.

Problem 102SE Diamonds sold at retail. Refer to the data for 308 diamonds saved in the file. Two quantitative variables in the data set are number of carats and selling price. One of the qualitative variables is the independent certification body that assessed each of the stones. Three certification bodies were used: GIA, IGI, and HRD. The Minitab printout shown below gives the means and standard deviations of the quantitative variables for each certification body. a. Construct a 95% confidence interval for the difference between the mean carat size of diamonds certified by GIA and the mean carat size of diamonds certified by HRD. b. Interpret the result, part a. Specifically, which (if either) of the two population means compared is larger and by how much? c. Construct a 95% confidence interval for the difference between the mean carat size of diamonds certified by GIA and the mean carat size of diamonds certified by IGI. d. Interpret the result, part c. Specifically, which (if either) of the two population means is larger and by how much? e. Construct a 95% confidence interval for the difference between the mean selling price of diamonds certified by HRD and the mean selling price of diamonds certified by IGI. f. Interpret the result, part e. Specifically, which (if either) of the two population means is larger and by how much? g. Conduct a test to determine whether the variation in carat size differs for diamonds certified by GIA and diamonds certified by HRD. Use ? = .05. h. Conduct a test to determine whether the variation in carat size differs for diamonds certified by GIA and diamonds certified by IGI. Use ? = .05. i. Conduct a test to determine whether the variation in selling price differs for diamonds certified by HRD and diamonds certified by IGI. Use ? = .05. j. Use a statistical software package (and the data in the accompanying file) to determine whether the assumption of normally distributed data for each certification group is reasonably satisfied.

Problem 106SE Turnover rates in the United States and Japan. High job turnover rates are often associated with high product defect rates because high turnover rates mean more inexperienced workers who are unfamiliar with the company’s product lines (Stevenson, Production/Operations Management, 2000). In a study, five Japanese and five U.S. plants that manufacture air conditioners were randomly sampled; their turnover rates are listed in the table. a. Do the data provide sufficient evidence to indicate that the mean annual percentage turnover for U.S. plants exceeds the corresponding mean percentage for Japanese plants? Test using ? = .05. b. Find and interpret the observed significance level of the test you conducted in part a. c. List any assumptions you made in conducting the hypothesis test of part a. Comment on their validity for this application.

Problem 103SE Ages of cable TV shoppers. Refer to the International Association for Time Use Research study on cable TV viewers who purchase items from one of the home shopping channels, Exercise 7.142 (p. 412). The 1,600 sampled viewers described their motivation for watching cable TV shopping networks by giving their level of agreement (on a 5-point scale, where 1 = strongly disagree and 5 = strongly agree) with the statement, “I have nothing else to do.” The researcher wanted to compare the mean responses of viewers who watch the shopping network at noon with those viewers who do not watch at noon. a. Give the null and alternative hypotheses for determining whether the mean response of noontime watchers differs from the mean response of non-noontime watchers. b. The researcher found the p-value for the test, part a, to be .02. Interpret this result, assuming ? = .05. c. Interpret the result, part b, assuming ? = .01. d. The sample means for noontime watchers and non-watchers were found to be 3.3 and 3.4, respectively. Comment on the practical significance of this result.

Sampling plan for a movie promotion. Advertising companies often try to characterize the average user of a client’s product so ads can be targeted at particular segments of the buying community. A new movie is about to be released, and the advertising company wants to determine whether to aim the ad campaign at people under or over 25 years of age. It plans to arrange an advance showing of the movie to an audience from each group and then obtain an opinion about the movie from each individual. How many individuals should be included in each sample if the advertising company wants to estimate the difference in the proportions of viewers in each age group who will like the movie to within .05 with 90% confidence? Assume the sample size for each group will be the same and about half of each group will like the movie.

Problem 104SE Career success expectations. In evaluating the usefulness and validity of a questionnaire, researchers often pretest the questionnaire on different independently selected samples of respondents. Knowledge of the differences and similarities of the samples and their respective populations is important for interpreting the questionnaire’s validity. Educational and Psychological Measurement (Feb. 1998) reported on a questionnaire developed for measuring the career success expectations of employees. The instrument was tested on the two independent samples described in the following table. a. Does the population of managers and professionals from which the sample was drawn consist of more males than the part-time MBA population does? Conduct the appropriate test using ? = .05. b. Describe any assumptions you made in conducting the test of part a and why you made them. c. Does the population of managers and professionals consist of more married individuals than the part-time MBA population does? Conduct the appropriate hypothesis test using ? = .01. d. What assumptions must hold for the test of part c to be valid?

Problem 107SE Cell phone usage differs by gender. The role of the cell phone in modern life was investigated by a Pew Internet & American Life Project (April 2006) survey. A total of 1,286 cell phone users were interviewed in the sample. One of the objectives was to compare male and female cell phone users. For example, 32% of men admitted they sometimes don’t drive safely while talking or texting on a cell phone compared to 25% of women. Also, 71% of men used their cell phone in an emergency compared to 77% of women. Assume that half (643) of the cell phone users in the sample were men and half (643) were women. a. Describe the two populations of interest in the survey. b. Give an estimate of the proportion of men and the proportion of women who sometimes do not drive safely while talking or texting on a cell phone. c. Find a 90% confidence interval for the difference between the proportions of men and women who sometimes do not drive safely while talking or texting on a cell phone. d. From your answer to part c, can you conclude that men are more likely than women to sometimes not drive safely while talking or texting on a cell phone? Explain. e. Give an estimate of the proportion of men and the proportion of women who used their cell phone in an emergency. f. Conduct a test to determine whether the proportions of men and women who used their cell phone in an emergency differ. Use ? = .10.

Likelihood of getting a routine medical checkup. Who is more likely to get a routine medical checkup—employed or unemployed people? To answer this question, a team of physicians and public health professors collected data on a sample of over 2,200 individuals (American Journal of Public Health, Jan. 2002). Of the 1,140 individuals who were employed, 642 visited a physician for a routine checkup within the past year. In contrast, 740 of the 1,106 unemployed individuals had a routine medical checkup within the past year. a. Specify the parameter of interest to the research team. b. Set up the null and alternative hypotheses for testing whether there is a difference between the percentages of employed and unemployed people who had a recent routine medical checkup. c. Compute the test statistic for the test. d. Give the rejection region for the test using \(\alpha\ =\ .01\). e. The research team reported the p-value for the test as p-value \(\approx\) 0. Do you agree? f. Make the appropriate conclusion.

Problem 109SE Comparing purchasers and nonpurchasers of toothpaste. Marketing strategists would like to predict consumer response to new products and their accompanying promotional schemes. Consequently, studies that examine the differences between buyers and nonbuyers of a product are of interest. One classic study conducted by Shuchman and Riesz (Journal of Marketing Research) was aimed at characterizing the purchasers and nonpurchasers of Crest toothpaste. The researchers demonstrated that both the mean household size (number of persons) and mean household income were significantly larger for purchasers than for nonpurchasers. A similar study used independent random samples of size 20 and yielded the data shown in the following table on the age of the householder primarily responsible for buying toothpaste. a. Do the data present sufficient evidence to conclude there is a difference in the mean age of purchasers and nonpurchasers? Use a = .10. b. What assumptions are necessary in order to answer part a? c. Find the observed significance level for the test and interpret its value. d. Calculate and interpret a 90% confidence interval for the difference between the mean ages of purchasers and nonpurchasers.

Problem 110SE Killing moths with carbon dioxide. A University of South Florida biologist conducted an experiment to determine whether increased levels of carbon dioxide kill leaf-eating moths (USF Magazine, Winter 1999). Moth larvae were placed in open containers filled with oak leaves. Half the containers had normal carbon dioxide levels, while the other half had double the normal level of carbon dioxide. Ten percent of the larvae in the containers with high carbon dioxide levels died, compared to 5% in the containers with normal levels. Assume that 80 moth larvae were placed, at random, in each of the two types of containers. Do the experimental results demonstrate that an increased level of carbon dioxide is effective in killing a higher percentage of leaf-eating moth larvae? Test using ? = .01.

Problem 111SE Racial profiling by the LAPD. Racial profiling is a term used to describe any police action that relies on ethnicity rather than behavior to target suspects engaged in criminal activities. Does the Los Angeles Police Department (LAPD) invoke racial profiling in stops and searches of LA drivers? This question was addressed in Chance (Spring 2006). a. Data on stops and searches of both African Americans and white drivers are summarized in the accompanying table. Conduct a test (at ? = .05) to determine if there is a disparity in the proportions of African American and white drivers who are searched by the LA police after being stopped. b. The LAPD defines a hit rate as the proportion of searches that result in a discovery of criminal activity. Use the data in the table to estimate the disparity in the hit rates for African American and white drivers using a 95% confidence interval. Interpret the results.

State SAT scores. Refer to Exercise 2.27 (p. 60) and the data on average math SAT scores for each of the 50 states and District of Columbia for the years 2001 and 2011. The data are saved in the file. (The first five observations and last two observations in the data set are shown in the table below.) a. In Exercise 2.27 c, you computed the paired differences of SAT scores by subtracting the 2001 score from the 2011 score for each state. Find the mean of these 51 paired differences. This value is \(\mu_{d}\), the mean difference in SAT scores for the population of 50 states and the District of Columbia. b. Explain why there is no need to employ the confidence interval or test procedures of this section to make an inference about \(\mu_{d}\). c. Now, suppose the 50 paired differences of part a represent a sample of SAT score differences for 50 randomly selected high school students. Use the data in the file to make an inference about whether the true mean SAT score of high school students in 2011 differs from the true mean in 2001. Use a confidence level of 90. Text Transcription: mu_d

Environmental impact study. Some power plants are located near rivers or oceans so that the available water can be used for cooling the condensers. Suppose that, as part of an environmental impact study, a power company wants to estimate the difference in mean water temperature between the discharge of its plant and the offshore waters. How many sample measurements must be taken at each site to estimate the true difference between means to within .2°C with 95% confidence? Assume that the range in readings will be about 4°C at each site and the same number of readings will be taken at each site.

Rat damage to sugarcane fields. Poisons are used to prevent rat damage in sugarcane fields. The U.S. Department of Agriculture is investigating whether the rat poison should be located in the middle of the field or on the outer perimeter. One way to answer this question is to determine where the greater amount of damage occurs. If damage is measured by the proportion of cane stalks that have been damaged by rats, how many stalks from each section of the field should be sampled to estimate the true difference between proportions of stalks damaged in the two sections to within .02 with 95% confidence?

Instrument precision. When new instruments are developed to perform chemical analyses of products (food, medicine, etc.), they are usually evaluated with respect to two criteria: accuracy and precision. Accuracy refers to the ability of the instrument to identify correctly the nature and amounts of a product’s components. Precision refers to the consistency with which the instrument will identify the components of the same material. Thus, a large variability in the identification of a single batch of a product indicates a lack of precision. Suppose a pharmaceutical firm is considering two brands of an instrument designed to identify the components of certain drugs. As part of a comparison of precision, 10 test-tube samples of a well-mixed batch of a drug are selected and then 5 are analyzed by instrument A and 5 by instrument B. The data shown below are the percentages of the primary component of the drug given by the instruments. Do these data provide evidence of a difference in the precision of the two machines? Use \(\alpha\ =\ .10\).

Computer-mediated communication study. Computer-mediated communication (CMC) is a form of interaction that heavily involves technology (e.g., instant messaging, e-mail). A study was conducted to compare relational intimacy in people interacting via CMC to people meeting face-to-face (FTF) (Journal of Computer-Mediated Communication, April 2004). Participants were 48 undergraduate students, of which half were randomly assigned to the CMC group and half assigned to the FTF group. Each group was given a task that required communication with the group members. Those in the CMC group used the “chat” mode of instant-messaging software; those in the FTF group met in a conference room. The variable of interest, relational intimacy score, was measured (on a 7-point scale) for each participant after each of three different meeting sessions and is saved in the accompanying file. Scores for the first meeting session are given in the table on the next page. The researchers hypothesized that, after the first meeting, the mean relational intimacy score for participants in the CMC group would be lower than the mean relational intimacy score for participants in the FTF group. Test the researchers’ hypothesis using \(\alpha\) = .10. .

Problem 122SE CareerBank.com annual salary survey. CareerBank.com conducts an annual salary survey of accounting, finance, and banking professionals. For one survey, data were collected for 2,800 responses submitted online by professionals across the country who voluntarily responded to CareerBank.com’s Web-based survey. Salary comparisons were made by gender, education, and marital status. Some of the results are shown in the accompanying table. a. Suppose you want to make an inference about the difference between the mean salaries of male and female accounting/finance/banking professionals at a 95% level of confidence. Why is this impossible to do using the information in the table? b. Give values of the missing standard deviations that would lead you to conclude that the mean salary for males is significantly higher than the mean salary for females at a 95% level of confidence. c. In your opinion, are the sample standard deviations, part b, reasonable values for the salary data? Explain. d. How does the data-collection method impact any inferences derived from the data?

Gambling in public high schools. With the rapid growth in legalized gambling in the United States, there is concern that the involvement of youth in gambling activities is also increasing. University of Minnesota Professor Randy Stinchfield compared the rates of gambling among Minnesota public school students between 1992 and 1998 (Journal of Gambling Studies, Winter 2001). Based on survey data, the table (next column) shows the percentages of ninth-grade boys who gambled weekly or daily on any game (e.g., cards, sports betting, lotteries) for the 2 years. a. Are the percentages of ninth-grade boys who gambled weekly or daily on any game in 1992 and 1998 significantly different? (Use \(\alpha\ =\ .01\).) b. Professor Stinchfield states that “because of the large sample sizes, even small differences may achieve statistical significance, so interpretations of the differences should include a judgment regarding the magnitude of the difference and its public health significance.” Do you agree with this statement? If not, why not? If so, obtain a measure of the magnitude of the difference between 1992 and 1998 and attach a measure of reliability to the difference.

Computer-mediated communication study (cont’d). Refer to Exercise 8.116. The researchers also hypothesized that the mean relational intimacy score for participants in the group would significantly increase between the first and third meetings, but the difference between the first and third meetings would not significantly change for participants in the FTF group. a. For the CMC group comparison, give the null and alternative hypotheses of interest. b. The researchers made the comparison, part a, using a paired t-test. Explain why the data should be analyzed as matched pairs. c. For the CMC group comparison, the reported test statistic was t = 3.04 with p-value = .003. Interpret these results. Is the researchers’ hypothesis supported? d. For the FTF group comparison, give the null and alternative hypotheses of interest. e. For the FTF group comparison, the reported test statistic was t = .39 with p-value = .70. Interpret these results. Is the researchers’ hypothesis supported?

Salaries of postgraduates. Refer to the Economics of Education Review (Vol. 21, 2002) study of the relationship between education level and earnings, Exercise 7.46 (p. 379). A National Adult Literacy Survey revealed that males with a postgraduate degree had a sample mean salary of $61,340 (with standard error \(S_{\bar{x}_M}\ =\ $2,185\)), while females with a postgraduate degree had a sample mean salary of $32,227 (with standard error \(S_{\bar{x}_F}\ =\ $932\)). Let \(\mu_M\) represent the population mean salary of all males with postgraduate degrees and \(\mu_F\) represent the population mean salary of all females with postgraduate degrees. a. Set up the null and alternative hypotheses for determining whether \(\mu_M\) exceeds \(\mu_F\). b. Calculate the test statistic for the test, part a. [Note: \(s_{\overline{\bar{X}}_{\mathrm{M}} -\bar{x}_{\mathrm{F}}}=\sqrt{\left(\mathrm{s}_{\bar{x}_{\mathrm{M}}}^{2}+s_{\overline{\bar{x}}_{\mathrm{F}}}^{2}\right)}\).] c. Find the rejection region for the test using \(\alpha\ =\ .01\). d. Use the results, parts b and c, to make the appropriate conclusion.

Problem 119SE Impact of gender on advertising. How does gender affect the type of advertising that proves to be most effective? An article in the Journal of Advertising Research (May/June 1990) makes reference to numerous studies that conclude males tend to be more competitive with others than with themselves. To apply this conclusion to advertising, the author created two ads promoting a new brand of soft drink: Ad 1: Four men are shown competing in racquetball Ad 2: One man is shown competing against himself in racquetball The author hypothesized that the first ad would be more effective when shown to males. To test this hypothesis, 43 males were shown both ads and asked to measure their attitude toward the advertisement (Aad), their attitude toward the brand of soft drink (Ab), and their intention to purchase the soft drink (Intention). Each variable was measured using a 7-point scale, with higher scores indicating a more favorable attitude. The results are shown in the table below. Do you agree with the author’s hypothesis?

Positive spillover effects from self-managed work teams. To improve quality, productivity, and timeliness, many American industries employ self-managed work teams (SMWTs). A team typically consists of 5 to 15 workers who are collectively responsible for making decisions and performing all tasks related to a particular project. Because SMWTs require that employees be trained in interpersonal skills, they can have potential positive spillover effects on a worker’s family life. The link between SMWT work characteristics and workers’ perceptions of positive spillover into family life was investigated in the Quality Management Journal (Summer 1995). Survey data were collected from 114 AT&T employees who work in 1 of 15 SMWTs at an AT&T technical division. The workers were divided into two groups: (1) those who reported positive spillover of work skills to family life and (2) those who did not report positive work spillover. The two groups were compared on a variety of job and demographic characteristics, one of which was the use of creative ideas (measured on a 7-point scale, where the larger the number, the more of the characteristic indicated). The data (simulated from summary information provided in the Quality Management Journal article) are saved in the file. a. One comparison of interest to the researchers is whether the mean creative use of ideas scale score for employees who report positive spillover of work skills to family life differs from the mean scale score for employees who did not report positive work spillover. Give the null and alternative hypotheses that will allow the researchers to make the comparison. b. Discuss whether it is appropriate to apply the large-sample z-test to test the hypotheses, part a. c. The results of the test are shown in the SPSS printout below. Interpret these results. Make the appropriate conclusion using \(\alpha\ =\ .05\). d. A 95% confidence interval for the difference between the mean use of creative ideas scale scores is shown in the last column of the SPSS printout. Interpret this interval. Does the inference derived from the confidence interval agree with that from the hypothesis test? e. The data also include the qualitative variable, Gender, for each worker. The researchers want to know whether the proportion of male workers in the two groups are significantly different. A Minitab printout of the analysis is shown below. Fully interpret the results in the words of the problem.

Problem 58E Predicting software defects. Refer to the PROMISE Software Engineering Repository data on 498 modules of software code written in “C” language for a NASA spacecraft instrument, saved in the file. (See Exercise 3.76, p. 168) Recall that the software code in each module was evaluated for defects; 49 were classified as “true” (i.e., module has defective code), and 449 were classified as “false” (i.e., module has correct code). Consider these to be independent random samples of software code modules. Researchers predicted the defect status of each module using the simple algorithm, “If number of lines of code in the module exceeds 50, predict the module to have a defect.” The accompanying SPSS printout shows the number of modules in each of the two samples that were predicted to have defects (PRED_LOC = “yes”) and predicted to have no defects (PRED_LOC = “no”). Now, define the accuracy rate of the algorithm as the proportion of modules that were correctly predicted. Compare the accuracy rate of the algorithm when applied to modules with defective code to the accuracy rate of the algorithm when applied to modules with correct code. Use a 99% confidence interval.