Food availability at middle schools. Most schools offer a

Problem 1E Under what circumstances is the sign test preferred to the t-test for making inferences about the central tendency of a population?

What is the probability that a randomly selected observation exceeds the a. Mean of a normal distribution? b. Median of a normal distribution? c. Mean of a nonnormal distribution? d. Median of a nonnormal distribution?

Consider the following sample of 10 measurements. Use these data to conduct each of the following sign tests using the binomial tables (Table I, Appendix D) and \(\alpha=.05\): a. \(H_{0}: \eta=9 \text { versus } H_{\mathrm{a}}: \eta>9\) b. \(H_{0}: \eta=9 \text { versus } H_{\mathrm{a}}: \eta \neq 9\) c. \(H_{0}: \eta=20 \text { versus } H_{\mathrm{a}}: \eta<20\) d. \(H_{0}: \eta=20 \text { versus } H_{\mathrm{a}}: \eta \neq 20\) e. Repeat each of the preceding tests using the normal approximation to the binomial probabilities. Compare the results. f. What assumptions are necessary to ensure the validity of each of the preceding tests?

Use Table I of Appendix D to calculate the following binomial probabilities: a. \(P(x \geq 7)\) when n = 8 and p = .5 b. \(P(x \geq 5)\) when n = 8 and p = .5 c. \(P(x \geq 8)\) when n = 8 and p = .5 d. \(P(x \geq 10)\) when n = 15 and p = .5. Also use the normal approximation to calculate this probability and then compare the approximation with the exact value. e. \(P(x \geq 15)\) when n = 25 and p = .5. Also use the normal approximation to calculate this probability and then compare the approximation with the exact value.

Self-managed work teams and family life. Refer to the Quality Management Journal (Summer 1995) study of self-managed work teams (SMWTs), discussed in Exercise 8.118 (p. 474). Recall that the researchers investigated the connection between SMWT work characteristics and workers’ perceptions of positive spillover into family life (one group of workers reported positive spillover of work skills to family life while another group did not report positive work spillover). The data collected on 114 AT&T employees are described below. In Exercise 8.118, you compared the two groups of workers on each characteristic using parametric methods. Reanalyze the data using nonparametrics. Are the job-related characteristics most highly associated with positive work spillover the same as those identified in Exercise 8.118? Comment on the validity of the parametric and nonparametric results.

Problem 5E Suppose you wish to conduct a test of the research hypothesis that the median of a population is greater than 75. You randomly sample 25 measurements from the population and determine that 17 of them exceed 75. Set up and conduct the appropriate test of hypothesis at the .10 level of significance. Be sure to specify all necessary assumptions.

Salaries of experienced MBA graduates. According to U.S. News & World Report’s Business School Rankings, the median earnings for graduates of full-time, highly ranked MBA programs 4 years after graduating is $125,000. A random sample of 50 recent graduates from a particular highly ranked MBA program was mailed a questionnaire and asked to report their annual earnings. Fifteen usable responses were received; nine indicated earnings greater than $125,000 and six indicated earnings below $125,000. a. Specify the null and alternative hypotheses that should be used in testing whether the median income of graduates of the MBA program is more than $125,000. b. Conduct the test of part a using \(\alpha = .05\) and draw your conclusion in the context of the problem. c. What assumptions must hold to ensure the validity of your hypothesis test?

Lobster trap placement. Refer to the Bulletin of Marine Science (April 2010) observational study of lobster trap placement by teams fishing for the red spiny lobster in Baja California Sur, Mexico, Exercise 7.52 (p. 384). Trap-spacing measurements (in meters) for a sample of seven teams of red spiny lobster fishermen are reproduced in the accompanying table. In Exercise 7.52, you tested whether the average of the trap-spacing measurements for the population of red spiny lobster fishermen fishing in Baja California Sur, Mexico, differs from 95 meters. a. There is concern that the trap-spacing data do not follow a normal distribution. If so, how will this impact the test you conducted in Exercise 7.52? b. Propose an alternative nonparametric test to analyze the data. c. Compute the value of the test statistic for the nonparametric test. d. Find the p-value of the test. e. Use the value of \(\alpha\) you selected in Exercise 7.52 and give the appropriate conclusion.

Short-sale stock returns. On July 15, 2008, the Securities and Exchange Commission (SEC) temporarily suspended short sales of stocks of several financial firms in order to protect the firms from sudden stock price declines. The impact the temporary restriction had on the New York Stock Exchange was the subject of an article published in the Journal of Financial Markets (Vol. 13, 2010). For one portion of the study, the researchers examined the daily abnormal stock returns for a sample of 17 stocks subject to the short-sale restrictions 1 month after the SEC announcement. Of these 17 stocks, 6 had a positive abnormal return rate. In theory, if the SEC restriction was effective, half of all stocks with suspended short sales would have positive return rates and half would have negative return rates. Is there evidence to dispute this theory? Test using \(\alpha = .05\).

Caffeine in Starbucks coffee. Researchers at the University of Florida College of Medicine investigated the level of caffeine in 16-ounce cups of Starbucks coffee (Journal of Analytical Toxicology, Oct. 2003). In one phase of the experiment, cups of Starbucks Breakfast Blend (a mix of Latin American coffees) were purchased on 6 consecutive days from a single specialty coffee shop. The amount of caffeine in each of the six cups (measured in milligrams) is provided in the table. 564 498 259 303 300 307 a. Suppose the scientists are interested in determining whether the median amount of caffeine in Breakfast Blend coffee exceeds 300 milligrams. Set up the null and alternative hypotheses of interest. b. How many of the cups in the sample have a caffeine content that exceeds 300 milligrams? c. Assuming p = .5, use the binomial table in Appendix D to find the probability that at least four of the six cups have caffeine amounts that exceed 300 milligrams. d. Based on the probability, part c, what do you conclude about \(H_0\) and \(H_a\)? (Use \(\alpha\) = .05.)

Performance of stock screeners. Refer to Exercise 6.34 (p. 318). Recall that stock screeners are automated tools used by investment companies to help clients select a portfolio of stocks to invest in. The annualized percentage returns on investment (as compared to the Standard & Poor’s 500 Index) for 13 randomly selected stock screeners provided by the American Association of Individual Investors (AAII) are repeated below. a. In Exercise 6.34a, the t-distribution was used to find a 90% confidence interval for the average annualized percentage return on investment of all stock screeners provided by AAII. Explain why the resulting inference may be invalid. b. A positive annualized return reflects a stock portfolio that performed better than the S&P 500. State the null and alternative hypotheses for a nonparametric test designed to determine if more than half of all AAII stock screeners perform better than the S&P 500. c. Conduct the test, part b, using \(\alpha = .05\). Interpret your result in the context of the problem.

Radon exposure in Egyptian tombs. Refer to the Radiation Protection Dosimetry (December 2010) study of radon exposure in Egyptian tombs, Exercise 7.53 (p. 384). The radon levels—measured in becquerels per cubic meter (\(\mathrm{Bq} / \mathrm{m}^{3}\))—in the inner chambers of a sample of 12 tombs are reproduced in the table below. Recall that for safety purposes, the Egypt Tourism Authority (ETA) temporar-ily closes the tombs if the level of radon exposure in the tombs rises too high, say \(6,000 Bq/m^3\). Conduct a non-parametric test to determine if the true median level of radon exposure in the tombs is less than \(6,000 Bq/m^3\). Use \(\alpha=.10\). Should the tombs be closed?

Suppose you wish to compare two treatments, A and B, based on independent random samples of 15 observations selected from each of the two populations. If \(T_1 = 173\), do the data indicate that distribution A is shifted to the left of distribution B? Test using \(\alpha = .05\).

Suppose you want to compare two treatments, A and B. In particular, you wish to determine whether the distribution for population B is shifted to the right of the distribution for population A. You plan to use the Wilcoxon rank sum test. a. Specify the null and alternative hypotheses you would test. b. Suppose you obtained the following independent random samples of observations on experimental units subjected to the two treatments. Conduct a test of the hypotheses described in part a. Test using \(\alpha\)=.05 .

Specify the test statistic and the rejection region for the Wilcoxon rank sum test for independent samples in each of the following situations: a. \(n 1=10, n 2=6, \alpha=.10 H 0\) : Two probability distributions, 1 and 2, are identical Ha: Probability distribution for population 1 is shifted to the right or left of the probability distribution for population 2 b. \(n 1=5, n 2=7, \alpha=.05\) H0: Two probability distributions, 1 and 2, are identical Ha: Probability distribution for population 1 is shifted to the right of the probability distribution for population 2 c. \(n 1=9, n 2=8, \alpha=.025\) H0: Two probability distributions, 1 and 2, are identical Ha: Probability distribution for population 1 is shifted to the left of the probability distribution for population 2 d. \(n 1=15, n 2=15, \alpha=.05 H 0\) : Two probability distributions, 1 and 2, are identical Ha: Probability distribution for population 1 is shifted to the right or left of the probability distribution for population 2

Independent random samples are selected from two populations. The data shown in the table. a. Use the Wilcoxon rank sum test to determine whether the data provide sufficient evidence to indicate a shift in the locations of the probability distributions of the sampled populations. Test using \(\alpha = .05\). b. Do the data provide sufficient evidence to indicate that the probability distribution for population 1 is shifted to the right of the probability distribution for population 2? Use the Wilcoxon rank sum test with \(\alpha = .05\).

Problem 12E Surface roughness of pipe. Refer to the Anti-Corrosion Methods and Materials (Vol. 50, 2003) study of the surface roughness of coated interior pipe used in oil fields, Exercise 6.33 (p. 318). The data (in micrometers) for 20 sampled pipe sections are reproduced in the table. Conduct a nonparametric test to determine whether the median surface roughness of coated interior pipe, h, differs from 2 micrometers. Test using ? = .05 1.72 2.50 2.16 2.13 1.06 2.24 2.31 2.03 1.09 1.40 2.57 2.64 1.26 2.05 1.19 2.13 1.27 1.51 2.41 1.95 Source: “Coated pipe interior surface roughness as measured by three scanning probe instruments,” by T. Pesacreta and F. Farshad, in ANTI-CORROSION METHODS AND MATERIALS, 2003.

Problem 13E Ranking PhD programs in economics. Refer to the Southern Economic Journal (Apr. 2008) rankings of 129 PhD programs in economics, Exercise 2.103 (p. 90). Recall that the number of publications published by faculty teaching in the PhD program and the quality of the publications were used to develop an overall productivity score for each PhD program. The following table gives the z-scores for the 10 PhD programs that specialize in agricultural and natural resource economics. Assume these 10 programs represent a random sample of all PhD programs that specialize in agricultural and natural resource economics. Give your opinion on whether the median productivity z-score of all such PhD programs differs from 0. Test using ? = .05. School z-Score 1 North Carolina State 0.37 2 Iowa State 0.35 3 Wyoming -0.30 4 SUNY Binghamton -0.48 5 Tulane -0.65 6 Hawaii, Manoa -0.69 7 New Mexico -0.71 8 Rhode Island -0.72 9 Utah State -0.73 10 Colorado School of Mines -0.76 Source: THE SOUTHERN ECONOMIC JOURNAL, April 2009.

Short Message Service for cell phones. Short Message Service (SMS) is the formal name for the communication service that allows the interchange of short text messages between mobile telephone devices. About 75% of mobile phone subscribers worldwide send or receive SMS text messages. Consequently, SMS provides an opportunity for direct marketing. In Management Dynamics (2007), marketing researchers investigated the perceptions of college students toward SMS marketing. For one portion of the study, the researchers applied the Wilcoxon rank sum test to compare the distributions of the number of text messages sent and received during peak time for two groups of cell phone users: those on an annual contract and those with a pay-as-you-go option. a. Specify the null hypothesis tested in the words of the problem. b. Give the formula for the large-sample test statistic if there were 25 contract users and 40 pay-as-you-go users in the sample. c. The Wilcoxon test results led the researchers to conclude “that contract users sent and received significantly more SMS messages during peak time than pay-as-you-go users.” Based on this information, draw a graph that is representative of the two SMS usage rate populations.

Problem 19E Bursting strength of bottles. Polyethylene terephthalate (PET) bottles are used for carbonated beverages. A critical property of PET bottles is their bursting strength (i.e., the pressure at which bottles filled with water burst when pressurized). In the Journal of Data Science (May 2003), researchers measured the bursting strength of PET bottles made from two different designs—an old design and a new design. The data (pounds per square inch) for 10 bottles of each design are shown in the table. Suppose you want to compare the distributions of bursting strengths for the two designs. a. Rank all 20 observed pressures from smallest to largest and assign ranks from 1 to 20. b. Sum the ranks of the observations from the old design. c. Sum the ranks of the observations from the new design. d. Compute the Wilcoxon rank sum statistic. e. Carry out a nonparametric test (at ? = .05) to compare the distribution of bursting strengths for the two designs.

Gender attitudes toward corruption and tax evasion. Do men and women differ in their attitudes toward public corruption and tax evasion? This was the question of interest in a study published in Contemporary Economic Policy (Oct. 2010). The data for the analysis were obtained from a representative sample of over 30,000 Europeans. Each person was asked how justifiable it is for someone to (1) accept a bribe in the course of his or her duties and (2) cheat on his or her taxes. Responses were measured as 0, 1, 2, or 3, where 0 = “always justified” and 3 = “never justified.” The large-sample Wilcoxon rank sum test was applied in order to compare the response distributions of men and women. a. Give the null hypothesis for the test in the words of the problem. b. An analysis of the “justifiability of corruption” responses yielded a large-sample test statistic of z = -14.10 with a corresponding p-value of approximately 0. Interpret this result. c. Refer to part b. Women had a larger rank sum statistic than men. What does this imply about gender attitudes toward corruption? d. An analysis of the “justifiability of tax evasion” responses yielded a large-sample test statistic of z = -18.12 with a corresponding p-value of approximately 0. Interpret this result. e. Refer to part d. Again, women had a larger rank sum statistic than men. What does this imply about gender attitudes toward tax evasion?

The X-Factor in golf performance. Many golf teaching professionals believe that a greater hip-to-shoulder differential angle during the early downswing—dubbed the “X-Factor”—leads to improved golf performance. The Journal of Quantitative Analysis in Sports (Vol. 5, 2009) published an article on the X-Factor and its relationship to golfing performance. The study involved 15 male golfers with a player handicap of 20 strokes or fewer. The golfers were divided into two groups: 8 golfers with a handicap of 10 strokes or fewer (low-handicapped group) and 7 golfers with a handicap between 12 and 20 strokes (high-handicapped group). The X-Factor, i.e., the hip-to-shoulder differential angle (in degrees), was measured for each golfer at the top of the backswing during his tee-shot. The researchers hypothesized that low-handicapped golfers will tend to have higher X-Factors than high-handicapped golfers. The researchers also discovered that the sample data were not normally distributed. Consequently, they applied a nonparametric test. a. What nonparametric test is appropriate for analyzing these data? b. Specify the null and alternative hypotheses of interest in the words of the problem. c. Give the rejection region for this test, using \(\alpha = .05\). d. The researchers reported a p-value of .487. Use this result to draw a conclusion.

Homework assistance for accounting students. Refer to the Journal of Accounting Education (Vol. 25, 2007) study on homework assistance for accounting students, Exercise 8.18 (p. 444). Recall that 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, the students were all given a test on the subject, and the knowledge gains (improvement in test scores) determined. The accompanying table gives the sample median knowledge gains for the three groups of students. a. The researchers theorized that as the level of homework assistance increases, the test score improvement will decrease. Do the sample medians reported in the table support this theory? b. What is the problem with using only the sample medians to make inferences about the population median knowledge gains for the three groups of students? c. The researchers conducted the Wilcoxon rank sum test to compare the median knowledge gain of students in the “no solutions” group with the median 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 nonparametric test of part c was reported as .456. Using \(\alpha = .05\), interpret this result. Text Transcription: alpha = .05

Children’s recall of TV ads. Refer to the Journal of Advertising (Spring 2006) study of children’s recall of tele-vision advertisements, Exercise 8.15 (p. 434). 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. The number of 10 specific items from the ad recalled correctly by each child is shown in the table. Recall that the researchers theorized that children who receive an audiovisual presentation will have the same level of recall as those who receive only the visual aspects of the ad. Consider testing the researchers’ theory using the Wilcoxon rank sum test. a. Set up the appropriate null and alternative hypotheses for the test. b. Find the value of the test statistic. c. Give the rejection region for \(\alpha=.10\). d. Make the appropriate inference. What can you say about the researchers’ theory?

Teamwork between nurses and doctors. In the treatment of critically ill patients, teamwork among health care professionals is essential. What is the level of collaboration between nurses and resident doctors working in the intensive care unit (ICU)? This was the question of interest in an article published in the Journal of Advanced Nursing (Vol. 67, 2011). Independent samples of 31 nurses and 46 resident doctors, all working in the ICU, completed the Baggs Collaboration and Satisfaction about Care Decisions survey. Responses to all questions were measured on a 7-point scale, where 1 = never and 7 = always. The data for the following two questions (simulated from information provided in the article) are listed at the bottom of the page. a. Conduct a nonparametric test (at \(\alpha = .05\)) to compare the response distributions for nurses and doctors on Question 4. Practically interpret the result. b. Conduct a nonparametric test (at \(\alpha = .05\)) to compare the response distributions for nurses and doctors on Question 5. Practically interpret the result.

Does rudeness really matter in the workplace? Refer to the Academy of Management Journal (Oct. 2007) study on rudeness in the workplace, Exercise 8.21 (p. 436). Recall that 98 college students enrolled in a management course were randomly assigned to one of two experimental conditions: rudeness condition (where students were berated by a facilitator for being irresponsible and unprofessional) and control group (no facilitator comments). Each student was asked to write down as many uses for a brick as possible in 5 minutes. The data are reproduced in the next table. a. Show that although the data for the rudeness condition are approximately normally distributed, the control group data are skewed. b. Conduct the appropriate nonparametric test (at \(\alpha=.01\)) to determine if the true median performance level for students in the rudeness condition is lower than the true median performance level for students in the control group. c. Explain why the parametric 2-sample test conducted in Exercise 8.21 is appropriate even though the data for both groups are not normally distributed. (Note that the nonparametric and parametric tests yield the same conclusions.)

Patent infringement case. Refer to the Chance (Fall 2002) study of a patent infringement case brought against Intel Corp., Exercise 8.19 (p. 435). Recall that the case rested on whether a patent witness’s signature was written on top of key text in a patent notebook or under the key text. Using an X-ray beam, zinc measurements were taken 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 lines—are reproduced in the table. a. Why might the Student’s t-procedure you applied in Exercise 8.19 be inappropriate for analyzing this data? b. Use a nonparametric test (at a = .05) to compare the distribution of zinc measurements for the text line with the distribution for the intersection. c. Use a nonparametric test (at a = .05) to compare the distribution of zinc measurements for the witness line with the distribution for the intersection. d. From the results, parts b and c, what can you infer about the median zinc measurements at the three notebook locations?

Specify the test statistic and the rejection region for the Wilcoxon signed rank test for the paired difference design in each of the following situations: a. n = 30, \(\alpha\) = .10 \(H_0\): Two probability distributions, 1 and 2, are identical \(H_a\): Probability distribution for population 1 is shifted to the right or left of probability distribution for population 2 b. n = 20, \(\alpha\) = .05 \(H_0\): Two probability distributions, 1 and 2, are identical \(H_a\): Probability distribution for population 1 is shifted to the right of the probability distribution for population 2 c. n = 8, \(\alpha\) = .005 \(H_0\): Two probability distributions, 1 and 2, are identical \(H_a\): Probability distribution for population 1 is shifted to the left of the probability distribution for population 2

Suppose you wish to test a hypothesis that two treatments, A and B, are equivalent against the alternative that the responses for A tend to be larger than those for B. a. If the number of pairs equals 25, give the rejection region for the large-sample Wilcoxon signed rank test for \(\alpha = .05\). b. Suppose that \(T_+ = 273\). State your test conclusions. c. Find the p-value for the test and interpret it.

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). Recall that 70 children who were ill with an upper respiratory tract infection were given either a dosage of dextromethorphan (DM) — an over-the-counter cough medicine — or a similar dose of honey. 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) are reproduced in the accompanying table. The researchers concluded that “honey may be a preferable treatment for the cough and sleep difficulty associated with childhood upper respiratory tract infection.” Use the nonparametric method presented in this section to analyze the data (use \(\alpha = .05\)). Do you agree with the researchers?

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). The data on engine heat rate (kilojoules per kilowatt per hour) are saved in the accompanying file. Recall that the researchers classified gas turbines into three categories: traditional, advanced, and aeroderivative. Suppose you want to compare the heat rate distributions for traditional and aeroderivative turbine engines. a. Demonstrate that the assumptions required to compare the mean heat rates using a t-test are likely to be violated. b. A Minitab printout of the nonparametric test to compare the two heat rate distributions is shown below. Interpret the p-value of the test shown at the bottom of the printout.

A paired difference experiment with n = 30 pairs yielded \(T_+ = 354\). a. Specify the null and alternative hypotheses that should be used in conducting a hypothesis test to determine whether the probability distribution for population 1 is located to the right of that for population 2. b. Conduct the test of part a using \(\alpha = .05\). c. What is the approximate p-value of the test of part b? d. What assumptions are necessary to ensure the validity of the test you performed in part b?

Suppose you want to test a hypothesis that two treatments, A and B, are equivalent against the alternative hypothesis that the responses for A tend to be larger than those for B. You plan to use a paired difference experiment and to analyze the resulting data using the Wilcoxon signed rank test. a. Specify the null and alternative hypotheses you would test. b. Suppose the paired difference experiment yielded the data in the table. Conduct the test of part a. Test using \(\alpha = .025\).

Twinned drill holes. Refer to the Exploration and Mining Geology (Vol. 18, 2009) study of drill twinned holes, Exercise 8.33 (p. 445). Recall that the drilling of a new hole, or “twin,” next to an earlier drill hole is a traditional method of verifying mineralization grades. The data in the table represent total amount of heavy minerals (THM) percentages for a sample of 15 twinned holes drilled at a diamond mine in Africa. In Exercise 8.33 you used a confidence interval based on Student’s t-distribution to check for a difference in the true THM means of all original holes and their twin holes drilled at the mine. a. Explain why the results of the confidence interval may be invalid. b. What is the appropriate nonparametric test to apply? State \(H_0\) and \(H_a\) for the test. c. Compute the difference between the “1st hole” and “2nd hole” measurements for each drilling location. d. Rank the differences, part c. e. Compute the rank sums of the positive and negative differences. f. Use the rank sums, part e, to conduct the nonparametric test at \(\alpha = .05\). Can the geologists conclude that there is no evidence of a difference in the THM distributions of all original holes and their twin holes drilled at the mine?

Problem 34E Performance ratings of government agencies. Refer to The Public Manager (Summer 2008) performance ratings of government agencies, Exercise 8.32 (p. 445). Evaluation scores for all agencies were obtained for two consecutive years and are saved in the file. Data for a random sample of five of these agencies are shown in the table on the next page. Suppose you want to determine whether the distribution of evaluation scores in year 2 is shifted above the distribution of evaluation scores in year 1. a. Specify the null and alternative hypotheses for a Wilcoxon signed rank test of the data. b. In Exercise 8.32b you computed the difference between the two scores for each sampled agency. Now rank the absolute values of these differences. c. Sum the ranks of the positive differences, part b. Also, sum the ranks of the negative differences. d. Use the results, part c, to find the test statistic. e. Give the rejection region for the test using ? = .05. f. Make the appropriate conclusion in the words of the problem. Agency Year 1 Score Year 2 Score GSA 34 40 Agriculture 33 35 HHS 37 35 USAID 32 42 Defense 17 32 Source: “Performance ratings of government agencies,” by J. Ellig and H. Wray, from Measuring Performance Reporting Quality. THE PUBLIC MANAGER, Vol. 37.2, Summer 2008, p. 66. Copyright © 2008 by Jerry Ellig. Reprinted with permission.

Healing potential of handling museum objects. Does handling a museum object have a positive impact on a sick patient’s well-being? To answer this question, researchers at the University College London collected data from 32 sessions with hospital patients (Museum & Society, Nov. 2009). Each patient’s health status (measured on a 100-point scale) was recorded both before and after handling museum objects such as archaeological artifacts and brass etchings. The data (simulated) are listed in the accompanying table. The Wilcoxon signed rank test was applied to the data with the results shown in the accompanying SPSS printout. a. Use the information in the printout to find the large sample Wilcoxon signed rank test statistic. b. Does handling a museum object have a positive impact on a sick patient’s well-being? Test using \(\alpha=.01\).

Impact of red-light cameras on car crashes. Refer to the June 2007 Virginia Department of Transportation (VDOT) study of a newly adopted photo-red-light enforcement program, Exercise 8.40 (p. 447). Recall that 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 inter-section per year) for 13 intersections in Fairfax County, VA, are reproduced in the table on the next page. The VDOT wants to determine if the photo-red enforcement program is effective in reducing red-light-running crash incidents at intersections. Use the nonparametric Wilcoxon signed rank test (and the accompanying Minitab printout) to analyze the data for the VDOT. Data for Exercise 15.37

Food availability at middle schools. Most schools offer a la carte food items in the cafeteria for students at lunch. To encourage students to eat healthy, the U.S. Department of Agriculture (USDA) requires schools to offer nutritional food items. Two methods for identifying and quantifying food items in the a la carte line—a detailed inventory approach and a checklist approach—were compared in the Journal of School Health (Dec. 2009). Data were collected for a sample of 37 middle schools. For each school, the accompanying table gives the percentage of a la carte food items deemed healthy as determined by both methods. The researchers used a nonparametric analysis to determine if the distribution of healthy food item percentages using the inventory method is shifted above or below the distribution of healthy food item percentages using the checklist method. If no significant difference is detected, the checklist method will be recommended since it is simpler and requires less resources. Conduct the appropriate analysis at \(\alpha = .05\). Which method do you recommend?

Taking “power naps” during work breaks. According to the National Sleep Foundation, companies are encouraging their workers to take “power naps” (Athens Daily News, Jan. 9, 2000). In Exercise 8.37 (p. 446), you analyzed data collected by a major airline that had recently begun encouraging reservation agents to nap during their breaks. 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 are reproduced in the table below. Compare the distributions of number of complaints for the two time periods using the Wilcoxon signed rank test. Use \(\alpha = .05\) to make the appropriate inference.

Concrete pavement response to temperature. Civil engineers at West Virginia University have developed a 3D model to predict the response of jointed concrete pavement to temperature variations (The International Journal of Pavement Engineering, Sep. 2004). To validate the model, model predictions were compared to field measurements on key concrete stress variables taken at a newly constructed highway. One variable measured was slab top transverse strain (i.e., change in length per unit length per unit time) at a distance of 1 meter from the longitudinal joint. The 5-hour changes (8:20 p.m. to 1:20 a.m.) in slab top transverse strain for 6 days are listed in the table below. Analyze the data using a nonparametric test. Is there a shift in the change in transverse strain distributions between field measurements and the 3D model? Test using \(\alpha = .05\).

NHTSA new car crash tests. Refer to the National Highway Traffic Safety Administration (NHTSA) crash test data for new cars. In Exercise 8.36 (p. 446) you compared the chest injury ratings of drivers and front-seat passengers using the Student’s t-procedure for matched pairs. Suppose you want to make the comparison for only those cars that have a driver’s star rating of 5 stars (the highest rating). The data for these 18 cars are listed in the table below. Now consider analyzing these data using the Wilcoxon signed rank test. a. State the null and alternative hypotheses. b. Use a statistical software package to find the signed rank test statistic. c. Give the rejection region for the test using \(\alpha = .01\). d. State the conclusion in practical terms. Report the p-value of the test.

Teachers who involve parents. Teachers Involve Parents in Schoolwork (TIPS) is an interactive homework process designed to improve the quality of homework assignments for elementary, middle, and high school students. TIPS homework assignments require students to conduct interactions with family partners (parents, guardians, etc.) while completing the homework. Frances Van Voorhis (Johns Hopkins University) conducted a study to investigate the effects of TIPS in science and mathematics homework assignments (April 2001). Each large group of middle school students was assigned to complete TIPS homework assignments. At the end of the study, all students reported on the level of family involvement in their homework on a 4-point scale (0 = Never, 1 = Rarely, 2 = Sometimes, 3 = Frequently, 4 = Always). The data for science and math for a random sample of 10 students selected from the large group are shown in the table. Conduct a nonparametric analysis to compare the level of family involvement in science and math homework assignments of TIPS students. Use \(\alpha = 05\).

Under what circumstances does the \(\chi^{2}\) distribution provide an appropriate characterization of the sampling distribution of the Kruskal-Wallis H-statistic?

Data were collected from three populations, A, B, and C, using a completely randomized design. The following describes the sample data: \(n_{\mathrm{A}}=n_{\mathrm{B}}=n_{\mathrm{C}}=15\) \(R_{\mathrm{A}}=230 \quad R_{\mathrm{B}}=440 \quad R_{\mathrm{C}}=365\) a. Specify the null and alternative hypotheses that should be used in conducting a test of hypothesis to determine whether the probability distributions of populations A, B, and C differ in location. b. Conduct the test of part a. Use \(\alpha = .05\). c. What is the approximate p-value of the test of part b? d. Compute H using the alternative formula given in the footnote on the previous page. Verify that this formula yields the same value of H that you obtained in part b.

Suppose you want to use the Kruskal-Wallis H-test to compare the probability distributions of three populations. The following data represent independent random samples selected from the three populations: a. What type of experimental design was used? b. Specify the null and alternative hypotheses you would test. c. Specify the rejection region you would use for your hypothesis test, at \(\alpha = .01\). d. Conduct the test at \(\alpha = .01\). Text Transcription: alpha = .01

Containing wildfires. The International Journal of Wildland Fire (Dec. 2011) published a study of the time it takes to contain wildfires, both with and without aerial support. Containment time (in hours) was estimated by fire management personnel for a particular wildfire scenario that had no aerial support. Fire management personnel were classified according to one of three primary roles—ground, office, or air support. Data for 21 fire managers (simulated, based on information provided in the article) are listed in the table. One objective is to compare the estimated containment times of the three groups of fire managers. a. Why is the ANOVA F-test of Chapter 9 inappropriate for analyzing these data? Use graphs to support your answer. b. What is the appropriate nonparametric test to apply? State \(H_0\) and \(H_a\) for the test. c. Rank the 21 estimated containment times, and then find the rank sums for the three groups of fire managers. d. Compute the nonparametric test statistic. e. Find the rejection region for the test using \(\alpha = .10\). f. State the appropriate conclusion.

Study of recall of TV commercials. Refer to the Journal of Applied Psychology (June 2002) study of recall of television commercials, Exercise 9.79 (p. 547). In a designed experiment, 324 adults were randomly assigned to one of three viewer groups: (1) watch a TV program with a violent content code (V) rating, (2) watch a show with a sex content code (S) rating, and (3) watch a neutral TV program. The number of brand names recalled in the commercial messages was recorded for each participant. a. Give the null and alternative hypotheses for a Kruskal-Wallis test applied to the data. b. The results of the nonparametric test are shown in the Minitab printout on the next page. Locate the test statistic and p-value on the printout. c. Interpret the results, part b, using \(\alpha = .01\). What can the researchers conclude about the three groups of TV ad viewers?

Public defenders’ salaries. Random samples of seven lawyers employed as public defenders were selected from each of three major cities. Their salaries are recorded in the table on the next page. You have been hired to determine whether differences exist among the salary distributions for public defenders in the three cities. a. Under what circumstances would it be appropriate to use the F-test for a completely randomized design to perform the required analysis? b. Which assumptions required by the F-test are likely to be violated in this problem? Explain. c. Use the Kruskal-Wallis H-test to determine whether the salary distributions differ among the three cities. Specify your null and alternative hypotheses and state your conclusions in the context of the problem. Use \(\alpha = .05\). d. What assumptions are necessary to ensure the validity of the nonparametric test in part c?

Office rental growth rates. Real estate market cycles are commonly divided into four phases that are based on the rate of change of the demand for and supply of properties: I—Recovery, II—Expansion, III—Hypersupply, and IV—Recession. Glenn Mueller of Johns Hopkins University studied the office market cycles of U.S. real estate markets (Journal of Real Estate Research, July/Aug. 1999). For each of the four market cycles, office rental growth rates (i.e., growth rates for asking rents) were measured for a sample of six different real estate markets. These data (in percentages) are presented in the table below. a. Specify the null hypothesis for a Kruskal-Wallis test. b. Rank the 24 measurements in the data set. c. Find the rank sums and calculate the test statistic. d. Give the rejection region for the test at \(\alpha = .05\). e. Is there sufficient evidence to conclude that the distributions of office rental growth rates differ among the four market cycle phases? f. What are the advantages and disadvantages of applying the Kruskal-Wallis H-test in part a rather than the parametric F-test of Chapter 9?

Relieving pain with hypnosis. Rehabilitation medicine researchers at the University of Washington investigated whether virtual-reality hypnosis can relieve pain in trauma patients (International Journal of Clinical and Experimental Hypnosis, Vol. 58, 2010). Study participants were 20 patients treated at a major Level 1 trauma center. The patients were randomly assigned to one of three treatment groups: (1) VRH—virtual-reality hypnosis with posthypnotic suggestions for pain reduction, (2) VRD—virtual-reality distraction from pain without hypnotic suggestions for pain reduction, and (3) Control—no virtual-reality hypnosis, but standard care. Pain intensity was measured (on a 100-point scale) prior to treatment and 1 hour after treatment. The differences in pain-intensity levels (before minus after) are listed in the accompanying table. a. Conduct a nonparametric test to determine whether the distribution of differences in pain-intensity levels differs for the three treatments. Test using \(\alpha = .05\). What do you conclude? b. Combine the patients in the VRD and Control groups into a single treatment group (called non-posthypnotic suggestion). Compare the VRH treatment patients to the patients in this new group using the appropriate nonparametric test (using \(\alpha = .05\)). What do you conclude?

Commercial eggs produced from different housing systems. Refer to the Food Chemistry (Vol. 106, 2008) study of commercial eggs produced from different housing systems for chickens, Exercise 9.33 (p. 511). Recall that the four housing systems investigated were (1) cage, (2) barn, (3) free range, and (4) organic. Twenty-eight commercial grade-A eggs were randomly selected from supermarkets—10 of which were produced in cages, 6 in barns, 6 with free range, and 6 organic. A number of quantitative characteristics were measured for each egg, including penetration strength (newtons). The data (simulated from summary statistics provided in the journal article) are given below. a. Rank the observations in the data set from 1 to 28. b. Sum the ranks of the data for each housing system. c. Use the rank sums to find the Kruskal-Wallis test statistic. d. Based on the result, part c, what do you infer about the strength distributions of the four housing systems?

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 15.28 (p. 15-17). In addition to the two experimental groups of children with an upper respiratory tract infection—one that was given a dosage of dextromethorphan (DM) and the other a similar dose of honey—a third group of children received no dosage (control group). The cough symptoms improvement scores for the children are reproduced in the accompanying table. Conduct a nonparametric test to compare the distributions of cough improvement scores for the three dosage groups. Use \(\alpha=.01\).

Data were collected using a randomized block design with four treatments (A, B, C, and D) and b = 6. The following rank sums were obtained: \(R_{\mathrm{A}}=11 \quad \quad R_{\mathrm{B}}=21 \quad \quad R_{\mathrm{C}}=21 \quad \quad R_{\mathrm{D}}=7\) a. How many blocks were used in the experimental design? b. Specify the null and alternative hypotheses that should be used in conducting a hypothesis test to determine whether the probability distributions for at least two of the treatments differ in location. c. Conduct the test of part b. Use \(\alpha = .10\). d. What is the approximate p-value of the test of part c? e. Compute the value of the \(F_{\mathrm{r}} \text {-test }\) statistic using the alternative formula given in the footnote on p. 15-31. Verify that the test statistic is the same as that you obtained in part c.

Suppose you have used a randomized block design to help you compare the effectiveness of three different treatments, A, B, and C. You obtained the data given in the table below and plan to conduct a Friedman Fr-test. a. Specify the null and alternative hypotheses you will test. b. Specify the rejection region for the test. Use \(\alpha\) = .10. c. Conduct the test and interpret the results. Treatment Block A B C 1 9 11 18 2 13 13 13 3 11 12 12 4 10 15 16 5 9 8 10 6 14 12 16 7 10 12 15

An experiment was conducted using a randomized block design with four treatments and six blocks. The ranks of the measurements within each block are shown in the table below. Use the Friedman Fr-test for a randomized block design to determine whether the data provide sufficient evidence to indicate that at least two of the treatment probability distributions differ in location. Test using \(\alpha\) = .05. Block Treatment 1 2 3 4 5 6 1 3 3 2 3 2 3 2 1 1 1 2 1 1 3 4 4 3 4 4 4 4 2 2 4 1 3 2

Homework assistance for accounting students. Refer to the Journal of Accounting Education (Vol. 25, 2007) study of assisting accounting students with their homework, Exercise 15.22 (p. 15-15). A completely randomized design was employed, with students randomly assigned to receive one of three different levels of assistance on the homework: (1) the completed solution, (2) check figures at various steps of the solution, and (3) no help at all. The response variable of interest to the researchers was the knowledge gain (or, test score improvement). The data (simulated from descriptive statistics published in the article) are saved in the file. Analyze the data with the appropriate nonparametric method. Interpret the results, practically. Does your conclusion agree with the inferences drawn from the parametric analysis in Exercise 9.30 (p. 510)?

Estimating time needed to complete a task. In project management, a key concern is the length of time it takes to perform a certain task. Managers have found that estimating the time in a series of short segments generally leads to an underestimation of the total time. This theory was tested in a study published in Applied Cognitive Psychology (Vol. 25, 2011). Each in a sample of 10 subjects was asked to visualize walking a familiar route for about 20 minutes. Subjects were then asked to provide an estimate of the distance walked in several shorter time segments (e.g., in 45-second intervals) until the destination was reached. The total walking time was then determined by adding up the time segments required to reach the destination. All subjects estimated total walking time (in minutes) under each of four time-segment conditions: 45-second intervals, 2-minute intervals, 3-minute intervals, and 5-minute intervals. The data (simulated from information provided in the article) are listed in the table on the next page. The researchers want to know if the distribution of walking times differs for the four time segments. a. Explain why the data should be analyzed using Friedman’s test. b. A Minitab printout of the analysis is shown below. Locate the test statistic and p-value on the printout. c. Using \(\alpha = .01\), what conclusion can you draw from the test?

Rotary oil rigs. Refer to Exercise 9.58 (p. 530) and the World Oil (Jan. 2002) study of rotary oil rigs. Three months were randomly selected, and the number of oil rigs running in each of three states—California, Utah, and Alaska—was recorded. The data for the randomized block design are reproduced below. Consider a nonparametric test to compare the distributions of rotary oil rigs running in the three states. a. State the null and alternative hypotheses for the test. b. Rank the data within each month, then sum the ranks for each state. c. Use the rank sums from part b to find the value of the test statistic. d. Give the rejection region of the test at \(\alpha = .05\). e. State the conclusion in the words of the problem. Does the conclusion agree with that for the ANOVA F-test conducted in Exercise 9.58?

A new method of evaluating health care research reports. Refer to The Open Dentistry Journal (Vol. 4, 2010) study of a new method of evaluating health care research reports, Exercise 9.59 (p. 531). Recall that the assessment tool was validated on five systematic reviews (named R1, R2, R3, R4, and R5) on rheumatoid arthritis. For each review, scores on the 11 R-AMSTAR items (all measured on a 4-point scale) were obtained. The data are reproduced in the table below. One goal of the study was to compare the distribution of item scores for the five reviews. Conduct the analysis using the appropriate nonparametric test.

Problem 58E Conditions impeding farm production. A review of farmer involvement in agricultural research was presented in the Journal of Agricultural, Biological, and Environmental Statistics (Mar. 2001). In one study, each of six farmers ranked the level of farm production constraint imposed by five conditions: drought, pest damage, weed interference, farming costs, and labor shortage. The rankings, ranging from 1 (least severe) to 5 (most severe), and rank sums for the five conditions are listed in the table below. a. Use the rank sums shown in the table to compute the Friedman Fr statistic b. At ? = .05, find the rejection region for a test to compare the farmer opinion distributions for the five conditions. c. Make the proper conclusion, in the words of the problem.

Peer mentor training at a firm. Refer to the Journal of Managerial Issues (Spring 2008) study of the impact of peer mentor training at a large software company, Exercise 9.55 (p. 529). Recall that participants volunteered to attend a 1-day peer mentor training session. The trainee’s level of competence in peer mentoring (measured on a 7-point scale) was measured at three different times in the study: 1 week before training, 2 days after training, and 2 months after training. Data (simulated) for 15 trainees are displayed in the accompanying table. A Minitab nonparametric randomized block analysis is also provided below to compare the competence level distributions of the three time periods. a. Locate the rank sums on the printout. b. Use the rank sums to find the Friedman \(F_r\) statistic. c. Locate the test statistic and associated p-value on the printout. d. Conduct the test and give the appropriate conclusion in the words of the problem.

Quality of research methodology in medical journals. The journal eCAM (November 2006) published a study of the quality of the research methodology (e.g., statistical analysis) used in medical papers. For each in a sample of 13 research papers, the quality of the methodology on several dimensions was measured, with scores ranging from 1 (low quality) to 3 (high quality). The data in the table (next column) give the scores on three dimensions (labeled What, Who, and How) for each in a sample of 13 papers. Paper What Who How 1 3 2 2 2 3 1 3 3 2 1 1 4 2 2 2 5 2 2 1 6 2 1 2 7 2 2 2 8 2 1 3 9 1 2 1 10 2 1 2 11 2 1 3 12 2 2 1 13 3 2 2 Source: Table from “Evidence-based research in complementary and alternative medicine III: Treatment of patients with Alzheimer’s disease” by Francesco Chiapelli et al., in EVIDENCE-BASED COMPLEMENTARY AND ALTERNATIVE MEDICINE (Table 1) eCAM, 3.4, pp. 411-424. Copyright © 2006 by Francesco Chiapelli under a Creative Commons Attribution license. a. One goal of the study is to compare the mean scores of the three research methodology dimensions. Set up the null and alternative hypotheses for this test. b. Explain why the data should be analyzed using a nonparametric randomized block ANOVA. c. Conduct the analysis for the researchers. What do you conclude? (Use \(\alpha\) = .10.)

Reducing on-the-job stress. Refer to the Kansas State study designed to investigate the effects of plants on human stress levels, Exercise 9.60 (p. 531). The data (below) are given as finger temperatures for each of 10 students in a dimly lit room under three experimental conditions: presence of a live plant, presence of a plant photo, and absence of a plant (either live or photo). Analyze the data using a nonparametric procedure. Do students’ finger temperatures depend on the experimental condition?

Sealers used to retard metal corrosion. Corrosion of different metals is a problem in many mechanical devices. Three sealers used to help retard the corrosion of metals were tested to see whether there were any differences among them. Samples of 10 different metal compositions were treated with each of the three sealers, and the amount of corrosion was measured after exposure to the same environmental conditions for 1 month. The data are given in the table below. Is there any evidence of a difference in the probability distributions of the amounts of corrosion among the three types of sealer? Use \(\alpha\) = .05. Sealer Metal 1 2 3 1 4.6 4.2 4.9 2 7.2 6.4 7.0 3 3.4 3.5 3.4 4 6.2 5.3 5.9 5 8.4 6.8 7.8 6 5.6 4.8 5.7 7 3.7 3.7 4.1 8 6.1 6.2 6.4 9 4.9 4.1 4.2 10 5.2 5.0 5.1

Use Table XIV of Appendix D to find each of the following probabilities: a. \(P\left(r_{\mathrm{s}}>.508\right)\) when n = 22 b. \(P\left(r_{\mathrm{s}}>.448\right)\) when n = 28 c. \(P\left(r_{\mathrm{s}} \leq .648\right)\) when n = 10 d. \(P\left(r_{\mathrm{s}}<-.738 \text { or } r_{\mathrm{s}}>.738\right)\) when n = 8

Specify the rejection region for Spearman’s nonparametric test for rank correlation in each of the following situations: a. \(H_{0}: \rho=0 ; \quad H_{\mathrm{a}}: \rho \neq 0, n=10, \alpha=.05\) b. \(H_{0}: \rho=0 ; \quad H_{\mathrm{a}}: \rho>0, n=20, \alpha=.025\) c. \(H_{0}: \rho=0 ; \quad H_{\mathrm{a}}: \rho<0, n=30, \alpha=.01\)

The following sample data were collected on variables x and y: x 0 3 0 -4 3 0 4 y 0 2 2 0 3 1 2 a. Specify the null and alternative hypotheses that should be used in conducting a hypothesis test to determine whether the variables x and y are correlated. b. Conduct the test of part a using \(\alpha = .05\). c. What is the approximate p-value of the test of part b? d. What assumptions are necessary to ensure the validity of the test of part b? Text Transcription: alpha = .05

Problem 69E Compute Spearman’s rank correlation coefficient for each of the following pairs of sample observations:

Absentee rates at a jeans plant. Refer to Exercise 9.61 (p. 531) and the New Technology, Work, and Employment (July 2001) study of daily worker absentee rates at a jeans plant. Nine weeks were randomly selected and the absentee rate (percentage of workers absent) determined for each day (Monday through Friday) of the workweek. The data are reproduced in the table. Conduct a nonparametric analysis of the data to compare the distributions of absentee rates for the five days of the workweek. Week Monday Tuesday Wednesday Thursday Friday 1 5.3 1 1.9 1.3 1.6 2 12.9 9 2.6 0.4 0.5 3 0.8 1 5.7 0.4 1.4 4 2.6 0 4.5 10.2 4.5 5 24 10 11.3 13.6 14.1 6 9.1 5 7.5 2.1 9.3 7 11.1 4 4.1 4.2 4.1 8 9.5 7 4.5 9.1 12.9 9 4.8 5 10.0 6.9 9.0 Source: “The eradication of leisure,” by J. J. Boggis, in NEW TECHNOLOGY, WORK, AND EMPLOYMENT, 16.2, pp. 118-129, July 2011.

Extending the life of an aluminum smelter pot. Refer to the American Ceramic Society Bulletin (Feb. 2005) study of the life length of an aluminum smelter pot, Exercise 11.18 (p. 615). Because the life of a smelter pot depends on the porosity of the brick lining, the researchers measured the apparent porosity and the mean pore diameter of each of six bricks. The data are reproduced in the table in the next column. a. Rank the apparent porosity values for the six bricks. Then rank the six pore diameter values. b. Use the ranks, part a, to find the rank correlation between apparent porosity (y) and mean pore diameter (x). Interpret the result. c. Conduct a test for positive rank correlation. Use \(\alpha = .01\).

Software millionaires and birthdays. Refer to the analysis of the disproportionate number of software millionaires who were born around the year 1955, Exercise 11.19 (p. 615). Recall that on his Web blog (www.measuringusability.com), statistical consultant Jeff Sauro investigated this question by analyzing the data shown in the accompanying table. a. Compute Spearman’s rank correlation coefficient, \(r_s\), relating number (y) of software millionaire birthdays in a decade to total number (x) of U.S. births. b. Refer to part a. Is there evidence of positive rank correlation between y and x? Test using \(\alpha = .05\). c. Compute Spearman’s rank correlation coefficient, \(r_s\), relating number (y) of software millionaire birthdays in a decade to number (x) of CEO birthdays. d. Refer to part c. Is there evidence of positive rank correlation between y and x? Test using \(\alpha = .05\).

Rankings of marketing journals. College professors earn tenure by publishing in peer-reviewed academic journals. The rankings of these journals (often subjective) play a key role in the tenure process. A paper in the Journal of Informetrics (Vol. 4, 2010) investigated the merits of a new index designed for ranking journals and applied the index to recently published marketing journal articles. The new hg-index, based on Google Scholar searches, combines an assessment of both the quantity and quality of the papers published in the journal—the higher the hg-index score, the better the journal. This new index was compared to a count of the number of citations articles in the journal generated. Data on the hg-index score and number of citations for 20 (fictitious) marketing journals are provided in the table on the next page. The researchers used Spearman’s rank correlation to measure the association between the two methods of ranking marketing journals. a. Give one reason why the researchers’ used Spearman’s rank correlation rather than the usual (Pearson) correlation coefficient, r, from Chapter 11. b. Rank the 20 hg-index scores. c. Rank the 20 values of number of citations. d. Compute Spearman’s rank correlation coefficient, \(r_s\). Practically interpret this value. e. Conduct a test of hypothesis to determine if the true rank correlation in the population of all marketing journals is greater than 0. Test using \(\alpha = .01\).

Organizational use of the Internet. Researchers from the United Kingdom and Germany attempted to develop a theoretically grounded measure of organizational Internet use (OIU) and published their results in Internet Research (Vol. 15, 2005). Using data collected from a sample of 77 Web sites, they investigated the link between OIU level (measured on a 7-point scale) and several observation-based indicators. Spearman’s rank correlation coefficient (and associated p-values) for several indicators are shown in the table. a. Interpret each of the values of \(r_s\) given in the table. b. Interpret each of the p-values given in the table. (Use \(\alpha = .10\) to conduct each test.)

Problem 74E Food availability at middle schools. Refer to the Journal of School Health (Dec. 2009) study of identifying and quantifying food items in the a la carte line at a middle school, Exercise 15.38 (p. 15-24). Recall that two methods were compared—a detailed inventory approach and a checklist approach—for a sample of 36 middle schools. The data on percent of food items deemed healthy for each school are saved in the file. Use Spearman’s rank correlation coefficient to measure the strength of the association between the percentage determined using the inventory method and the percentage found using the checklist method. Conduct a test (at a = .05) for positive rank correlation.

Media coverage of the 9/11 attacks and public opinion. The terrorist attacks of September 11, 2001, and related events (e.g., the War in Iraq) have and continue to receive tremendous media coverage. How has this media coverage influenced the American public’s concern for terrorism? This was the topic of research conducted by journalism professors at the University of Missouri (International Journal of Public Opinion, Winter 2004). Using random-digit dialing, a telephone survey of Americans was conducted. Each person was asked to rate, on a scale of 1 to 5, his or her level of concern for each of eight topics: long war, future terrorist attacks, effect on economy, Israel-Palestine conflict, biological threats, air travel safety, war protests, and Afghan civilian deaths. The eight scores were summed to obtain a “public agenda” score. The respondents were also asked how many days per week they read the newspaper, watch the local television news, and watch national television news. The responses to these three questions were also summed to obtain a “media agenda” score. The researchers hypothesized that the public agenda score would be positively related to the media agenda score. Consider a small survey of n = 14 Americans. a. Spearman’s rank correlation between the two scores was computed to be rs = .643. Give a practical interpretation of this value. b. Refer to part a. Conduct Spearman’s rank correlation test of positive association at \(\alpha\) = .01. c. The researchers removed the “long war” question from the data and recomputed the “public agenda” score. Spearman’s rank correlation between the public agenda and the media agenda was then calculated as rs = .714. Conduct Spearman’s test for positive rank correlation using this value at \(\alpha\) = .01. Does the inference change?

America’s most reputable companies. Forbes magazine publishes a list of America’s most reputable companies based on an annual survey conducted by the Reputation Institute. The rankings are based on a “global pulse” score (the higher the score, the more reputable the company). Global pulse scores for the top 20 companies in 2011 and 2010 are listed in the table. Is there evidence of a positive rank correlation between global pulse scores of firms in 2011 and 2010? Use \(\alpha = .01\).

Assessmemt of biometric recognition methods. Biometric technologies have been developed to detect or verify an individual’s identity. These methods are based on physiological characteristics (called biometric signatures) such as facial features, eye irises, fingerprints, voice, hand shape, and gait. In Chance (Winter 2004), four biometric recognition algorithms were compared. All four methods were applied to 1,196 biometric signatures, and “match” scores were obtained. The Spearman correlation between match scores for each possible algorithm pair was determined. The rank correlation matrix is shown below. Interpret the results.

Sweetness of orange juice. Refer to the orange juice quality study, Exercise 11.22 (p. 616). Recall that a manufacturer that has developed a quantitative index of the “sweetness” of orange juice is investigating the relationship between the sweetness index and the amount of water-soluble pectin in the orange juice it produces. The data for 24 production runs at a juice manufacturing plant are reproduced in the preceding table. a. Calculate Spearman’s rank correlation coefficient between the sweetness index and the amount of pectin. Interpret the result. b. Conduct a nonparametric test to determine whether there is a negative association between the sweetness index and the amount of pectin. Use \(\alpha = .01\). Text Transcription: alpha = .01

Problem 75E In business, do nice guys finish first or last? Refer to the Nature (March 20, 2008) study of whether the saying “nice guys finish last” applies to business, Exercise 11.14 (p. 614). Recall that college students repeatedly played a version of the game “prisoner’s dilemma,” where competitors choose cooperation, defection, or costly punishment. At the conclusion of the games, the researchers recorded the average payoff and the number of times punishment was used by each player. The data in the table are representative of the data obtained in the study. The researchers concluded that “punishers tend to have lower payoffs.” Do you agree? Use Spearman’s rank correlation statistic to support your conclusion. Punish Payoff Punish Payoff 0 0.50 8 -0.20 1 0.20 10 0.15 2 0.30 12 -0.30 3 0.25 14 -0.10 4 0.00 16 -0.20 5 0.30 17 -0.25 6 0.10

The data for three independent random samples are shown in the table to the right. It is known that the sampled populations are not normally distributed. Use an appropriate test to determine whether the data provide sufficient evidence to indicate that at least two of the populations differ in location. Test using \(\alpha = .05\).

Two independent random samples produced the measurements listed in the table below. Do the data provide sufficient evidence to conclude that there is a difference between the locations of the probability distributions for the sampled populations? Test using \(\alpha\) =.05. Sample from Population 1 Sample from Population 2 1.2 1.0 1.5 1.9 1.9 1.8 1.3 2.7 .7 1.1 2.9 3.5 2.5

An experiment was conducted using a randomized block design with five treatments and four blocks. The data are shown in the table below. Do the data provide sufficient evidence to conclude that at least two of the treatment probability distributions differ in location? Test using \(\alpha = .05\).

Problem 81SE A random sample of nine pairs of observations are recorded on two variables, x and y. The data are shown in the table below. a. Do the data provide sufficient evidence to indicate that r, the rank correlation between x and y, differs from 0? Test using ? = .05. b. 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 19 12 2 27 19 3 15 7 4 35 25 5 13 11 6 29 10 7 16 16 8 22 10 9 16 18

Quality of white shrimp. In The American Statistician (May 2001), the nonparametric sign test was used to analyze data on the quality of white shrimp. One measure of shrimp quality is cohesiveness. Because freshly caught shrimp are usually stored on ice, there is concern that cohesiveness will deteriorate after storage. For a sample of 20 newly caught white shrimp, cohesiveness was measured both before storage and after storage on ice for 2 weeks. The difference in the cohesiveness measurements (before minus after) was obtained for each shrimp. If storage has no effect on cohesiveness, the population median of the differences will be 0. If cohesiveness deteriorates after storage, the population median of the differences will be positive. a. Set up the null and alternative hypotheses to test whether cohesiveness deteriorates after storage. b. In the sample of 20 shrimp, there were 13 positive differences. Use this value to find the p-value of the test. c. Make the appropriate conclusion (in the words of the problem) if \(\alpha = .05\).

Computer-mediated communication study (cont’d). Refer to Exercise 15.85. Relational intimacy scores (measured on a 7-point scale) were obtained for each participant after each of three different meeting sessions. The researchers hypothesized that relational intimacy scores for participants in the CMC group would tend to be higher at the third meeting than at the first meeting; however, they hypothesized that there would be no differences in scores between the first and third meetings for the FTF group. a. Explain why a nonparametric Wilcoxon signed rank test is appropriate for analyzing the data. b. For the CMC group comparison, give the null and alternative hypotheses of interest. c. Give the rejection region for conducting the test (at \(\alpha\) = .05), part b. Recall that there were 24 participants assigned to the CMC group. d. For the FTF group comparison, give the null and alternative hypotheses of interest. e. Give the rejection region for conducting the test (at \(\alpha\) = .05), part d. Recall that there were 24 participants assigned to the FTF group.

Problem 87SE RIF plan to fire older employees. Reducing the size of a company’s workforce in order to reduce costs is referred to as corporate downsizing or reductions in force (RIF) by the business community and media. Following RIFs, companies are often sued by former employees who allege that the RIFs were discriminatory with regard to age. Federal law protects employees over 40 years of age against such discrimination. Suppose one large company’s employees have a median age of 37. Its RIF plan is to fire 15 employees with ages listed in the table below. 43 32 39 28 54 41 50 62 22 45 47 54 43 33 59 a. Calculate the median age of the employees who are being terminated. b. What are the appropriate null and alternative hypotheses to test whether the population from which the terminated employees were selected has a median age that exceeds the entire company’s median age? c. Conduct the test of part b. Find the significance level of the test and interpret its value. d. Assuming that courts generally require statistical evidence at the .10 level of significance before ruling that age discrimination laws were violated, what do you advise the company about its planned RIF? Explain.

Forums for tax litigation. In litigating tax disputes with the IRS, taxpayers are permitted to choose the court forum. Three trial courts are available: (1) U.S. Tax Court, (2) Federal District Court, and (3) U.S. Claims Court. Accounting professors B. A. Billings (Wayne State University) and B. P. Green (University of Michigan-Dearborn) and business law professor W. H. Volz (Wayne State University) conducted a study of taxpayers’ choice of forum in litigating tax issues (Journal of Applied Business Research, Fall 1996). A random sample of 161 court decisions was obtained for analysis. Two of the many variables measured for each case were taxpayer’s choice of forum (Tax, District, or Claims Court) and tax deficiency DEF (i.e., the disputed amount, in dollars). a. The researchers applied a nonparametric test rather than a parametric test to compare the DEF distributions of the three tax litigation forums. Give a plausible reason for their choice. b. What nonparametric test is appropriate for this analysis? Explain. c. The table below summarizes the data analyzed by the researchers. Use the information in the table to compute the appropriate test statistic. d. The observed significance level (p-value) of the test was reported as p = .0037. Fully interpret this result.

Wine-tasting experiment. Two expert wine tasters were asked to rank six brands of wine. Their rankings are shown in the table in the next column. a. Use the rankings to compute \(r_s\). b. Do the data present sufficient evidence to indicate a positive correlation in the rankings of the two experts? Test using \(\alpha = .05\).

Employee suggestion system. An employee suggestion system is a formal process for capturing, analyzing, implementing, and recognizing employee-proposed organizational improvements. (The first known system was implemented by the Yale and Towne Manufacturing Company of Stamford, Connecticut, in 1880.) Using data from the National Association of Suggestion Systems, D. Carnevale and B. Sharp examined the strengths of the relationships between the extent of employee participation in suggestion plans and cost savings realized by employers (Review of Public Personnel Administration, Spring 1993). The data in the table are representative of the data they analyzed for a sample of federal, state, and local government agencies. Savings are calculated from the first year measurable benefits were observed. a. Explain why the savings data used in this study may understate the total benefits derived from the implemented suggestions. b. Carnevale and Sharp concluded that a significant moderate positive relationship exists between participation rates and cost savings rates in public sector suggestion systems. Do you agree? Test using \(\alpha = .01\) c. Justify the statistical methodology you used in part b.

Computer-mediated communication study. Refer to the Journal of Computer-Mediated Communication (Apr. 2004) study to compare those who interact via computer-mediated communication (CMC) to those who meet face-to-face (FTF), Exercise 8.116 (p. 473). Recall that 48 undergraduate students were randomly divided into the two groups. Those in the CMC group communicated using the “chat” mode of instant-messaging software; those in the FTF group met in a conference room. The relational intimacy scores (measured on a 7-point scale) of the participants are reproduced in the accompanying table. The researchers hypothesized that the relational intimacy scores for participants in the CMC group would tend to be lower than the relational intimacy scores for participants in the FTF group. a. Which nonparametric procedure should be used to analyze the data? b. Specify the null and alternative hypotheses of the test. c. Give the rejection region for the test using \(\alpha = .10\). d. Conduct the test and give the appropriate conclusion in the context of the problem.

Number-one-selling fast-food item. According to the National Restaurant Association, hamburgers are the number-one-selling fast-food item in the United States. An economist studying the fast-food-buying habits of Americans paid graduate students to stand outside two suburban McDonald’s restaurants near Boston and ask departing customers whether they spent more or less than $2.25 on hamburger products for their lunch. Twenty answered “less than”; 50 said “more than”; and 10 refused to answer the question. a. Is there sufficient evidence to conclude that the median amount spent for hamburgers at lunch at McDonald’s is less than $2.25? b. Does your conclusion apply to all Americans who eat lunch at McDonald’s? Justify your answer. c. What assumptions must hold to ensure the validity of your test in part a?

Designing an atlas. An atlas is a compendium of geographic, economic, and social information that describes one or more geographic regions. Atlases are used by the sales and marketing functions of businesses, local chambers of commerce, and educators. One of the most critical aspects of a new atlas design is its thematic content. In a survey of atlas users (Journal of Geography, May/June 1995), a large sample of high school teachers in British Columbia ranked 12 thematic atlas topics for usefulness. The consensus rankings of the teachers (based on the percentage of teachers who responded they “would definitely use” the topic) are given in the table. These teacher rankings were compared to the rankings of a group of university geography alumni made 3 years earlier. Compare the distributions of theme rankings for the two groups with an appropriate nonparametric test. Use \(\alpha = .05\). Interpret the results practically.

Satisfaction with MIS implementation. A management information system (MIS) is a computer-based information-processing system designed to support the operations, management, and decision functions of an organization. The development of an MIS involves three stages: definition, physical design, and implementation of the system. Thirty firms that recently implemented an MIS were surveyed: 16 were satisfied with the implementation results; 14 were not. Each firm was asked to rate the quality of the planning and negotiation stages of the development process, using a scale of 0 to 100, with higher numbers indicating better quality. (A score of 100 indicates that all the problems that occurred in the planning and negotiation stages were successfully resolved, while 0 indicates that none were resolved.) The results are shown in the table. a. Use the Wilcoxon rank sum test to compare the quality of the development processes of successfully and unsuccessfully implemented MISs. Test using \(\alpha = .05\). b. Under what circumstances could you use the two-sample t-test of Chapter 8 to conduct the same test?

School property tax rates. An economist is interested in knowing whether property tax rates differ among three types of school districts—urban, suburban, and rural. A random sample of several districts of each type produced the data in the table in the next column (rate is in mills, where 1 mill = $1/1,000). Do the data indicate a difference in the level of property taxes among the three types of school districts? Use \(\alpha = .05\).

Designing an atlas (cont’d). Refer to Exercise 15.92. In addition to high school teachers and university geography alumni, university geography students and representatives of the general public also ranked the 12 thematic topics. The rankings of all four groups are shown in the table in the next column. Compare the atlas theme ranking distributions of the four groups using a nonparametric test. Use \(\alpha=.10\).

Flexible working hours program. A job-scheduling innovation that has helped managers overcome motivation and absenteeism problems associated with a fixed 8-hour workday is a concept called flextime. This flexible working hours program permits employees to design their own 40- hour workweek to meet their personal needs. The management of a large manufacturing firm may adopt a flextime program depending on the success or failure of a pilot program. Ten employees were randomly selected and given a questionnaire designed to measure their attitude toward their job. Each was then permitted to design and follow a flextime workday. After 6 months, attitudes toward their jobs were again measured. The resulting attitude scores are displayed in the table. The higher the score, the more favorable the employee’s attitude toward his or her work. Use a nonparametric test procedure to evaluate the success of the pilot flextime program. Test using \(\alpha\) = .05. Employee Before After 1 54 68 2 25 42 3 80 80 4 76 91 5 63 70 6 82 88 7 94 90 8 72 81 9 33 39 10 90 93

Fluoride in drinking water. Many water treatment facilities supplement the natural fluoride concentration with hydro-fluosilicic acid in order to reach a target concentration of fluoride in drinking water. Certain levels are thought to enhance dental health, but very high concentrations can be dangerous. Suppose that one such treatment plant targets .75 milligrams per liter (mg/L) for their water. The plant tests 25 samples each day to determine whether the median level differs from the target. a. Set up the null and alternative hypotheses. b. Set up the test statistic and rejection region using \(\alpha = .10\). c. Explain the implication of a Type I error and a Type II error in the context of this application. d. Suppose that one day’s samples result in 18 values that exceed .75 mg/L. Conduct the test and state the appropriate conclusion in the context of this application. e. When it was suggested to the plant’s supervisor that a t-test should be used to conduct the daily test, she replied that the probability distribution of the fluoride concentrations was “heavily skewed to the right.” Show graphically what she meant by this and explain why this is a reason to prefer the sign test to the t-test.

Union negotiation preferences. A union wants to determine the preferences of its members before negotiating with management. Ten union members are randomly selected, and an extensive questionnaire is completed by each member. The responses to the various aspects of the questionnaire will enable the union to rank in order of importance the items to be negotiated. The rankings are shown in the next table. Conduct a nonparametric test to determine whether evidence exists that the probability distributions of ratings differ for at least two of the four negotiable items. Use \(\alpha=.05\).

Problem 98SE Does fatigue lead to more defectives? A manufacturer wants to determine whether the number of defectives produced by its employees tends to increase as the day progresses. Unknown to the employees, a complete inspection is made of every item that was produced on one day, and the hourly fraction defective is recorded. The resulting data are given in the next table. Do they provide evidence that the fraction defective increases as the day progresses? Test at the ? = .05 level. Hour Fraction Defective 1 .02 2 .05 3 .03 4 .08 5 .06 6 .09 7 .11 8 .10

Hazardous organic solvents. The Journal of Hazardous Materials (July 1995) published a study of the chemical properties of three different types of hazardous organic solvents used to clean metal parts. Independent samples of solvents from each of the three types—aromatics, chloralkanes, and esters—were collected. The data on sorption rates for the three solvents are listed in the table. Use a nonparametric test to compare the sorption rate distributions at \(\alpha = .01\).

Agent Orange and Vietnam vets. Agent Orange—the code name for an herbicide developed for the U.S. armed forces in the 1960s—was found to be extremely contaminated with TCDD, or dioxin. During the Vietnam War, an estimated 19 million gallons of Agent Orange was used to destroy the dense plant and tree cover of the Asian jungle. As a result of this exposure, many Vietnam veterans have dangerously high levels of TCDD in their blood and adipose (fatty) tissue. A study published in Chemosphere (Vol. 20, 1990) reported on the TCDD levels of 20 Massachusetts Vietnam vets who were possibly exposed to Agent Orange. The TCDD amounts (measured in parts per trillion) in both plasma and fat tissue of the 20 vets are listed in the accompanying table. a. Medical researchers consider a TCDD level of 3 parts per trillion (ppt) to be dangerously high. Do the data provide evidence (at \(\alpha = .05\)) to indicate that the median level of TCDD in the fat tissue of these Vietnam vets exceeds 3 ppt? b. Repeat part a for plasma. c. Medical researchers also are interested in comparing the TCDD levels in fat tissue and plasma for Vietnam veterans. Specifically, they want to determine if the distribution of TCDD levels in fat is shifted above or below the distribution of TCDD levels in plasma. Conduct this analysis (at \(\alpha = .05\)) and make the appropriate inference. d. Find the rank correlation between the TCDD level in fat tissue and the TCDD level in plasma. Is there sufficient evidence (at \(\alpha = .05\)) of a positive association between the two TCDD measures?

Comparing ethics of American and Mexican purchasing managers. In Mexico, the United States’ third largest trading partner, purchasing has not fully evolved into a profession with its own standards of ethical behavior. Researchers at Xavier University investigated the question: Do American and Mexican purchasing managers perceive ethical situations differently (Industrial Marketing Management, July 1999)? As part of their study, 15 Mexican purchasing managers and 15 American purchasing managers were asked to consider different ethical situations and respond on a 100-point scale with endpoints “strongly disagree” (1) and “strongly agree” (100). For the situation “accepting free trips from sales-people is okay,” the responses shown in the table were obtained. Do American and Mexican purchasing managers perceive the given ethical situation differently? Explain.