Rankings of MBA programs. Refer to the Business Ethics

A multinomial experiment with k = 4 cells and n = 205 produced the data shown in the one-way table below. a. Do these data provide sufficient evidence to conclude that the multinomial probabilities differ? Test using ? = .05. b. What are the Type I and Type II errors associated with the test of part a? c. Construct a 95% confidence interval for the multinomial probability associated with cell 3.

What are the characteristics of a multinomial experiment? Compare the characteristics to those of a binomial experiment.

A multinomial experiment with k = 3 cells and n = 320 produced the data shown in the following one-way table. Do these data provide sufficient evidence to contradict the null hypothesis that \(p_1=.25, p_2=.25\), and \(p_3=.50\)? Test using \(\alpha=.05\).

What conditions must n satisfy to make the test valid?

A “rigged” election? Chance (Spring 2004) presented data from a recent election held to determine the board of directors of a local community. There were 27 candidates for the board, and each of 5,553 voters was allowed to choose 6 candidates. The claim was that “a fixed vote with fixed percentages [was] assigned to each and every candidate, making it impossible to participate in an honest election.” Votes were tallied in six time slots: after 600 total votes were in, after 1,200, after 2,444, after 3,444, after 4,444, and, finally, after 5,553 votes. The data on three of the candidates (Smith, Coppin, and Montes) are shown in the accompanying table and saved in the RIGVOTE file. A residential organization believes that “there was nothing random about the count and tallies for each time slot, and specific unnatural or rigged percentages were being assigned to each and every candidate.” Give your opinion. Is the probability of a candidate receiving votes independent of the time slot, and if so, does this imply a rigged election?

Find the rejection region for a one-dimensional \(\chi^{2}\) test of a null hypothesis concerning \(p_{1}, p_{2}, \ldots, p_{k}\) k = 3 ; \(\alpha=.05\) k = 5 ; \(\alpha=.05\) k = 4 ; \(\alpha = .01\)

Mobile device typing strategies. Researchers estimate that in a typical month, about 75 billion text messages are sent in the United States. Text messaging on mobile devices (e.g., cell phones, smartphones) often requires typing in awkward positions that may lead to health issues. A group of Temple University public health professors investigated this phenomenon and published their results in Applied Ergonomics (March, 2012). One portion of the study focused on the typing styles of mobile device users. Typing style was categorized as (1) device held with both hands/both thumbs typing, (2) device held with right hand/right thumb typing, (3) device held with left hand/left thumb typing, (4) device held with both hands/right thumb typing, (5) device held with left hand/right index finger typing, or (6) other. In a sample of 859 college students observed typing on their mobile devices, the professors observed 396, 311, 70, 39, 18, and 25, respectively, in the six categories. Is this sufficient evidence to conclude that the proportions of mobile device users in the six texting style categories differ? Use ? = .10 to answer the question.

Museum management. Refer to the Museum Management and Curatorship (June 2010) worldwide survey of 30 leading museums of contemporary art. Recall that each museum manager was asked to provide the performance measure used most often for internal evaluation. A summary of the results is provided in the table and saved in the MUSEUM2 file. The data were analyzed using a chi-square test for a multinomial experiment. The results are shown in the MINITAB printout (bottom of the page). a. Is there evidence to indicate that one performance measure is used more often than any of the others? Test using ? = .10. b. Find a 90% confidence interval for the proportion of museums worldwide that use total visitors as their performance measure. Interpret the result. MINITAB Output

Rankings of MBA programs. Refer to the Business Ethics (Fall 2005) rankings of master in business administration (MBA) programs worldwide, Exercise 2.16 (p. 51). Recall that each of 30 business schools was rated according to student exposure to social and environmental issues in the classroom. Ratings ranged from 1 star (lowest-rated group) to 5 stars (highest-rated group). A summary of the star ratings assigned to the 30 MBA programs is reproduced in the table. a. Identify the categorical variable (and its levels) measured in this study. b. How many of the sampled MBA programs would you expect to observe in each star rating category if there are no differences in the category proportions in the population of all MBA programs? c. Specify the null and alternative hypotheses for testing whether there are differences in the star rating category proportions in the population of all MBA programs. d. Calculate the x2 test statistic for testing the hypotheses in part c. e. Give the rejection region for the test using ? = .05. f. Use the results, parts d and e, to make the appropriate conclusion. g. Find and interpret a 95% confidence interval for the proportion of all MBA programs that are ranked in the three-star category.

Survey on giving and volunteering. The National Tax Journal (Dec. 2001) published a study of charitable givers based on data collected from the Independent Sector Survey on Giving and Volunteering. A total of 1,072 charitable givers reported that their charitable contributions were motivated by tax considerations. The number of these 1,072 givers in each of 10 household income categories (saved in the accompanying file) is shown in the table below. a. If the true proportions of charitable givers in each household income group are the same, how many of the 1,072 sampled givers would you expect to find in each income category? b. Give the null hypothesis for testing whether the true proportions of charitable givers in each household income group are the same. c. Compute the chi-square test statistic for testing the null hypothesis, part b. d. Find the rejection region for the test if ? = .10. e. Give the appropriate conclusion for the test in the words of the problem.

Do social robots walk or roll? Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study of how engineers design social robots, Exercise 2.3 (p. 48). Recall that a social (or service) robot is designed to entertain, educate, and care for human users. In a random sample of 106 social robots obtained through a Web search, the researchers found that 63 were built with legs only, 20 with wheels only, 8 with both legs and wheels, and 15 with neither legs nor wheels. Prior to obtaining these sample results, a robot design engineer stated that 50% of all social robots produced have legs only, 30% have wheels only, 10% have both legs and wheels, and 10% have neither legs nor wheels. a. Explain why the data collected for each sampled social robot are categorical in nature. b. Specify the null and alternative hypotheses for testing the design engineer’s claim. c. Assuming the claim is true, determine the number of social robots in the sample that you expect to fall into each design category. d. Use the results to compute the chi-square test statistic. e. Make the appropriate conclusion using \(\alpha = .05\). Text Transcription: alpha = .05

Offshoring companies. “Offshoring” is a term that describes a company’s practice of relocating jobs and/or production to another country to reduce labor costs. The Journal of Applied Business Research (Jan/Feb 2011) published a study on the phenomenon of offshoring and how prevalent it is worldwide. The article included the results from a recent survey of CEOs at U.S. firms, where each CEO was asked about his or her firm’s position on offshoring. A summary of the results (similar to the actual study) is shown in the accompanying table. a. Identify the qualitative variable of interest (and its levels) for this study. b. Are the proportions of U.S. firms in the four offshoring position categories significantly different? Conduct the appropriate chi-square test using \(\alpha\ =\ .05\). c. Construct a 95% confidence interval for the proportion of U.S. firms who are currently offshoring. Interpret the result.

Profiling UK rental malls. Refer to the Urban Studies (June 2011) analysis of tenants renting space in United Kingdom regional shopping malls, Exercise 2.5 (p. 48) Recall that tenants were categorized into five different size groups based on amount of floor space: anchor tenants (more than 30,000 sq. ft.), major space users (between 10,000 and 30,000 sq. ft.), large standard tenants (between 4,000 and 10,000 sq. ft.), small standard tenants (between 1,500 and 4,000 sq. ft.), and small tenants (less than 1,500 sq. ft.). Suppose that a UK mall developer believes that the proportions of tenants in each category are .01, .05, .10, .40, and .44, respectively. In the actual study, 1,821 stores were sampled and the number of stores in each tenant category was reported as 14, 61, 216, 711, and 819, respectively. Use this information to test the mall developer’s belief (at \(\alpha\ =\ .01\)). What do you conclude?

Who is to blame for rising health care costs? Refer to Exercise 2.6 (p. 49) and The Harris Poll (Oct. 28, 2008) on who is to blame for the rising costs of healthcare. Recall that a nationwide survey of 2,119 U.S. adults answered the question “When you think of the rising costs of healthcare, who do you think is most responsible?” The responses are summarized in the table on the next page. One theory is that 50% of adults blame insurance companies, 10% blame pharmaceutical companies, 10% blame government, 10% blame hospitals, 10% blame physicians, 5% blame some other entity, and 5% are unsure. a. Explain why the data come from a multinomial experiment. b. Specify the null hypothesis for a test of the theory. c. Use statistical software to conduct the test using \(\alpha\ =\ .01\). What do you conclude?

Attitudes toward top corporate managers. Scandals involving large U.S. corporations (e.g., Enron, WorldCom, and Adelphia) have had a major impact on the public’s attitude toward business managers. In a Harris Poll administered immediately after the Enron scandal, a national sample of 2,023 adults were asked to agree or disagree with the following statement: “Top company managers have become rich at the expense of ordinary workers” (The Harris Poll, #55, Oct. 18, 2002). The response categories (and number of respondents in each) strongly agreed (1,173), somewhat agree (587), somewhat disagree (182), and strongly disagree (81). Suppose that prior to the Enron scandal, the percentages of all U.S. adults falling into the four response categories were 45%, 35%, 15%, and 5%, respectively. Is there evidence to infer that the percentages of all U.S. adults falling into the four response categories changed after the Enron scandal? Test using \(\alpha\ =\ .01\).

Coupon user study. A hot topic in marketing research is the exploration of a technology-based self-service (TBSS) encounter, e.g., ATMs, automated hotel checkout, online banking, and express package tracking. Marketing Professor Dan Ladik (University of Suffolk) investigated a customer’s motivation to use a TBSS developed for a firm’s discount coupons. The coupon users received the coupons in one of three ways—mail only (non technology user), Internet only (TBSS user), and both mail and Internet. One of the variables of interest in the study was Type of coupon user. In particular, the professor wants to know if the true proportions of mail only, Internet only, and both mail and Internet users differ. In a sample of 440 coupon users, the professor discovered that 262 received coupons via only mail, 43 via only the Internet, and 135 via both mail and Internet. Conduct the appropriate analysis for the professor. Use \(\alpha\ =\ .01\).

Cell phone user survey. If you subscribe to a cell phone plan, how many different cell phone numbers do you own? This was one question of interest in Public Opinion Quarterly (Vol. 70, No. 5, 2006). According to the Current Population Survey (CPS) Cell Phone Supplement, 51% of cell phone plans have only one cell number, 37% have two numbers, 9% have three numbers, and 3% have four or more numbers. An independent survey of 943 randomly selected cell phone users found that 473 pay for only one number, 334 pay for two numbers, 106 pay for three numbers, and 30 pay for four or more numbers. Conduct a test to determine if the data from the independent survey contradict the percentages reported by the CPS Cell Phone Supplement. Use \(\alpha\ =\ .01\).

Overloading in the trucking industry. Although illegal, overloading is common in the trucking industry. A state highway planning agency (Minnesota Department of Transportation) monitored the movements of overweight trucks on an interstate highway using an unmanned, computerized scale that is built into the highway. Unknown to the truckers, the scale weighed their vehicles as they passed over it. Each day’s proportion of 1 week’s total truck traffic (five-axle tractor truck semi trailers) is shown in the first column of the table below. During the same week, the number of overweight trucks per day is given in the second column. This information is saved in the accompanying file. The planning agency would like to know whether the number of overweight trucks per week is distributed over the 7 days of the week in direct proportion to the volume of truck traffic. Test using ? = .05.

Political representation of religious groups. Do those elected to the U.S. House of Representatives really “represent” their constituents demographically? This was a question of interest in Chance (Summer 2002). One of several demographics studied was religious affiliation. The accompanying table (saved in the USHOUSE file) gives the proportion of the U.S. population for several religions, as well as the number of the 435 seats in the House of Representatives affiliated with that religion. Give your opinion on whether or not the members of the House of Representatives are statistically representative of the religious affiliation of their constituents in the United States.

Find the rejection region for a test of independence of two classifications for which the contingency table contains r rows and c columns and a. r = 5, c = 5, \(\alpha\ =\ .05\) b. r = 3, c = 6, \(\alpha\ =\ .10\) c. r = 2, c = 3, \(\alpha\ =\ .01\)

Consider the following \(2\ \times\ 3\) (i.e., r = 2 and c = 3 ) contingency table shown below. a. Specify the null and alternative hypotheses that should be used in testing the independence of the row and column classifications. b. Specify the test statistic and the rejection region that should be used in conducting the hypothesis test of part a . Use \(\alpha\ =\ .01\). c. Assuming that the row classification and the column classification are independent, find estimates for the expected cell counts. d. Conduct the hypothesis test of part a. Interpret your result.

Refer to Exercise 10.20. a. Convert the frequency responses to percentages by calculating the percentage of each column total falling in each row. Also, convert the row totals to percentages of the total number of responses. Display the percentages in a table. b. Create a bar graph with row 1 percentage on the vertical axis and column number on the horizontal axis. Show the row 1 total percentage as a horizontal line on the graph. c. What pattern do you expect to see if the rows and columns are independent? Does the plot support the result of the test of independence in Exercise 10.20? Consider the following 2 × 3 (i.e., r = 2 and c = 3 ) contingency table:

Refer to Exercise 10.22. a. Convert the responses to percentages by calculating the percentage of each B class total falling into each A classification. b. Calculate the percentage of the total number of responses that constitute each of the A classification totals. c. Create a bar graph with row \(A_1\) percentage on the vertical axis and B classification on the horizontal axis. Does the graph support the result of the test of hypothesis in Exercise 10.22? Explain. d. Repeat part c for the row \(A_2\) percentages. e. Repeat part c for the row \(A_3\) percentages.

Test the null hypothesis of independence of the two classifications A and B of the 3 × 3 contingency table shown here. Use ? = .05.

Safety of hybrid cars. According to the Highway Loss Data Institute (HLDI), “Hybrid [automobiles] have a safety edge over their conventional twins when it comes to shielding their occupants from injuries in crashes” (HLDI Bulletin, Sept. 2011). Consider data collected by the HLDI on Honda Accords in 2002–2010. In a sample of 50,132 collision claims for conventional Accords, 5,364 involved injuries; in a sample of 1,505 collision claims for hybrid Accords, 137 involved injuries. You want to use this information to determine whether the injury rate for hybrid Accords is less than the injury rate for conventional Accords. a. Identify the two qualitative variables measured for each Honda Accord collision claim. b. Form a contingency table for this data, giving the number of claims in each combination of the qualitative variable categories. c. Give H0 and Ha for testing whether injury rate for collision claims depends on Accord model (hybrid or conventional). d. Find the expected number of claims in each cell of the contingency table, assuming that H0 is true. e. Compute the test statistic and compare your answer to the test statistic shown on the accompanying XLSTAT printout (next column). f. Find the rejection region for the test using ? = .05 and compare your answer to the critical value shown on the accompanying XLSTAT printout. XLSTAT Output for Exercise 10.24 g. Make the appropriate conclusion using both the rejection region method and the p-value (shown on the XLSTAT printout). h. Find a 95% confidence interval for the difference between the injury rates of conventional and hybrid Honda Accords. (See Section 10.3.) Use the interval to determine whether the injury rate for hybrid Accords is less than the injury rate for conventional Accords.

Purchasing souvenirs. A major tourist activity is shopping. Travel researchers estimate that nearly one-third of total travel expenditures are used on shopping for souvenirs (Journal of Travel Research, May 2011). To investigate the impact of gender on souvenir shopping, a survey of 3,200 tourists was conducted. One question asked how often the tourist purchases photographs, postcards, or paintings of the region visited. Responses were recorded as “Always,” “Often,” “Occasionally,” or “Rarely or Never.” The table shows the percentages of tourists responding in each category, by gender. a. Based on the percentages shown in the table, do you think male and female tourists differ in their responses to purchasing photographs, postcards, or paintings? Why are these percentages alone insufficient to draw a conclusion about the true response category proportions? b. Assume that 1,500 males and 1,700 females participated in the survey. Use these sample sizes and the percentages in the table to compute the counts of tourists in each of the Response/Gender categories. This represents the contingency table for the study. c. Specify the null and alternative hypotheses for testing whether male and female tourists differ in their responses to purchasing photographs, postcards, or paintings. d. An SPSS printout of the contingency table analysis is shown below. Locate the test statistic and p-value on the printout. e. Make the appropriate conclusion using \(\alpha = .01\). Text Transcription: alpha = .01

Stereotyping in deceptive and authentic news stories. Major newspapers lose their credibility (and subscribers) when they are found to have published deceptive or misleading news stories. In Journalism and Mass Communication Quarterly (Summer 2007), University of Texas researchers investigated whether certain stereotypes (e.g., negative references to certain nationalities) occur more often in deceptive news stories than in authentic news stories. The researchers analyzed 183 news stories that were proven to be deceptive in nature and 128 news stories that were considered authentic. Specifically, the researchers determined whether each story was negative, neutral, or positive in tone. The accompanying table gives the number of news stories found in each tone category. a. Find the sample proportion of negative tone news stories that are deceptive. b. Find the sample proportion of neutral news stories that are deceptive. c. Find the sample proportion of positive news stories that are deceptive. d. Compare the sample proportions, parts a–c. Does it appear that the proportion of news stories that are deceptive depends on story tone? Minitab output for Exercise 10.26 e. Give the null hypothesis for testing whether the authenticity of a news story depends on tone. f. Use the Minitab printout above to conduct the test, part e. Test at ? = .05.

Are travel professionals equitably paid? Business Travel News (July 17, 2006) reported the results of its annual Travel Manager Salary & Attitude survey. A total of 277 travel professionals, 103 males and 174 females, participated in the 2005 survey. One question asked for the travel professional’s opinion on the fairness of his/her salary. Responses were classified as “salary too low,” “equitable/ fair,” or “paid well.” The table below gives a breakdown of the responses in each category by gender. a. Find the proportion of male travel professionals who believe their salary is too low and compare it to the proportion of female travel professionals who believe their salary is too low. b. Repeat part a but compare the proportions who believe their salary is equitable/fair. c. Repeat part a but compare the proportions who believe they are paid well. d. Based on the comparisons, parts a–c, do you think opinion on the fairness of a travel professional’s salary differs for males and females? e. Refer to part d. Conduct the appropriate statistical test using ? = .10. f. Construct and interpret a 90% confidence interval for the difference between the proportions of part a.

Guilt in decision making. The effect of guilt emotion on how a decision maker focuses on a problem was investigated in the Jan. 2007 issue of the Journal of Behavioral Decision Making (see Exercise 3.44, p. 153). A total of 171 volunteer students participated in the experiment, where each was randomly assigned to one of three emotional states (guilt, anger, or neutral) through a reading/writing task. Immediately after the task, students were presented with a decision problem where the stated option had predominantly negative features (e.g., spending money on repairing a very old car). The results (number responding in each category) are summarized in the accompanying table. Is there sufficient evidence (at ? = .10) to claim that the option choice depended on emotional state? Use the data saved to answer the question.

Mobile device typing strategies. Refer to the Applied Ergonomics (March 2012) study of mobile device typing strategies, Exercise 10.11 (p. 570). Recall that typing style of mobile device users was categorized as (1) device held with both hands/both thumbs typing, (2) device held with right hand/right thumb typing, (3) device held with left hand/left thumb typing, (4) device held with both hands/right thumb typing, (5) device held with left hand/ right index finger typing, or (6) other. The researchers’ main objective was to determine if there are gender differences in typing strategies. Typing strategy and gender were observed for each in a sample of 859 college students observed typing on their mobile devices. The data are summarized in the accompanying table. Is this sufficient evidence to conclude that the proportions of mobile device users in the six texting style categories depend on whether a male or a female is texting? Use \(\alpha\ =\ .10\) to answer the question.

“Cry wolf” effect in air traffic controlling. Researchers at Alion Science Corporation and New Mexico State University collaborated on a study of how air traffic controllers respond to false alarms ( Human Factors , Aug. 2009). The researchers theorize that the high rate of false alarms regarding midair collisions leads to the “cry wolf” effect, i.e., the tendency for air traffic controllers to ignore true alerts in the future. The investigation examined data on a random sample of 437 conflict alerts. Each alert was first classified as a “true” or “false” alert. Then, each was classified according to whether or not there was a human controller response to the alert. The number of the 437 alerts that fall into each of the combined categories is given as follows: True alert/No response–3; True alert/Response–231; False alert/No response–37; False alert/ Response–166. This summary information is saved in the ATC file. Do the data indicate that the response rate of air traffic controllers to midair collision alarms differs for true and false alerts? Test using \(\alpha\ =\ .05\). What inference can you make concerning the “cry wolf” effect?

Eyewitnesses and mugshots. Refer to the Applied Psychology in Criminal Justice (April 2010) study of mugshot choices by eyewitnesses to a crime, Exercise 9.78 (p. 547). Recall that a sample of 96 college students was shown a video of a simulated theft, then asked to select a mugshot that most closely resembled the thief. The students were randomly assigned to view either 3, 6, or 12 mugshots at a time, with 32 students in each group. The number of students in the 3-, 6-, and 12-photos-per-page groups who selected the target mugshot were 19, 19, and 15, respectively. a. For each photo group, compute the proportion of students who selected the target mugshot. Which group yielded the lowest proportion? b. Create a contingency table for these data, with photo group in the rows and whether or not the target mugshot was selected in the columns. c. Analyze the contingency table, part b. Are there differences in the proportions who selected the target mugshot among the three photo groups? Test using \(\alpha\) = .10.

Offshoring companies. Refer to The Journal of Applied Business Research (Jan/Feb 2011) study of offshoring companies, Exercise 10.10 (p. 570). In addition to U.S. firms, CEOs from international companies were also surveyed on their offshoring positions. The number of firms in each position category (adapted from the results of the actual study) is shown in the accompanying table. Does a firm’s position on offshoring depend on the firm’s nationality? Test using \(\alpha\ =\ .05\).

Creating menus to influence others. The Journal of Consumer Research (Mar. 2003) published a study on influencing the choices of others by offering undesirable alternatives In one experiment conducted by the researcher, 96 subjects were asked to imagine that they had just moved to an apartment with two others and that they were shopping for a new appliance (e.g., a television, a microwave oven). Each subject was asked to create a menu of three brand choices for his or her roommates; then subjects were randomly assigned (in equal numbers) to one of three different “goal” conditions: (1) Create the menu in order to influence roommates to buy a preselected brand, (2) create the menu in order to influence roommates to buy a brand of your choice, and (3) create the menu with no intent to influence roommates. The researcher theorized that the menus created to influence others would likely include undesirable alternative brands. Consequently, the number of menus in each goal condition that was consistent with the theory was determined. The data are summarized in the accompanying table and saved in the MENU3 file. Analyze the data for the purpose of determining whether the proportion of subjects who select menus consistent with the theory depends on the goal condition. Use \(\alpha\ =\ .01\).

Problem 34E Coupon user study. Refer to the study of a customer’s motivation to use a technology-based self-service (TBSS) encounter developed for a firm’s discount coupons, Exercise 10.15 (p. 571). Recall that the coupon users received the coupons in one of three ways—mail only (nontechnology user), Internet only (TBSS user), and both mail and Internet. The researcher wants to know if there are differences in customer characteristics—specifically gender (male or female) and coupon usage satisfaction (satisfied, unsatisfied, or indifferent)—among the three types of coupon users. That is, does type of coupon user depend on gender? Does type depend on coupon usage satisfaction level? Data on these categorical variables were collected for a sample of 440 coupon users and are saved in the file. Conduct the appropriate analyses for the researcher. Use ? = .01 for each analysis. Present your conclusions in a professional report.

Examining the “Monty Hall Dilemma.” In Exercise 3.129 (p. 180), you solved the game show problem of whether or not to switch your choice of three doors—one of which hides a prize—after the host reveals what is behind a door not chosen. (Despite the natural inclination of many to keep one’s first choice, the correct answer is that you should switch your choice of doors.) This problem is sometimes called the “Monty Hall Dilemma,” named for Monty Hall, the host of the popular TV game show Let’s Make a Deal. In Thinking & Reasoning (Aug. 2007), Wichita State University professors set up an experiment designed to influence subjects to switch their original choice of doors. Each subject participated in 23 trials. In trial #1, three doors (boxes) were presented on a computer screen, only one of which hid a prize. In each subsequent trial, an additional box was presented, so that in trial #23, 25 boxes were presented. After selecting a box in each trial, all the remaining boxes except for one were either (1) shown to be empty (Empty condition), (2) disappeared (Vanish condition), (3) disappeared and the chosen box enlarged (Steroids condition), or (4) disappeared and the remaining box not chosen enlarged (Steroids2 condition). A total of 27 subjects were assigned to each condition. The number of subjects who ultimately switched boxes is tallied, by condition, in the table on the previous page for both the first trials and the last trial. a. For a selected trial, does the likelihood of switching boxes depend on condition? b. For a given condition, does the likelihood of switching boxes depend on trial number? c. Based on the results, parts a and b, what factors influence a subject to switch choices?

Classifying air threats with heuristics. The Journal of Behavioral Decision Making (Jan. 2007) published a study on the use of heuristics to classify the threat level of approaching aircraft. Of special interest was the use of a fast and frugal heuristic—a computationally simple procedure for making judgments with limited information—named “Take-the-Best-for-Classification” (TTBC).The subjects were 48 men and women, some from aCanadian Forces reserve unit, others university students. Each subject was presented with a radar screen on which simulated approaching aircraft were identified with asterisks. By using the computer mouse to click on the asterisk, one could receive further information about the aircraft. The goal was to identify the aircraft as “friend” or “foe” as fast as possible. Half the subjects were given cue-based instructions for determining the type of aircraft, while the other half were given pattern-based instructions. The researcher also classified the heuristic strategy used by the subject as TTB-C, Guess, or Other. Data on the two variables Instruction type and Strategy, measured for each of the 48 subjects, are saved in the AIRTHREAT file. (Data on the first and last five subjects are shown in the table below.) Do the data provide sufficient evidence at \(\alpha\ =\ .05\) to indicate that choice of heuristic strategy depends on type of instruction provided? How about at \(\alpha\ =\ .01\)?

A random sample of 150 observations was classified into the categories shown in the table below. a. Do the data provide sufficient evidence that the categories are not equally likely? Use \(\alpha\ =\ .10\). b. Form a 90% confidence interval for \(p_2\), the probability that an observation will fall into category 2.

Efficacy of an HIV vaccine. New, effective AIDS vaccines are now being developed using the process of “sieving” (i.e., sifting out infections with some strains of HIV). Harvard School of Public Health Statistician Peter Gilbert demonstrated how to test the efficacy of an HIV vaccine in Chance (Fall 2000). As an example, Gilbert reported the results of VaxGen’s preliminary HIV vaccine trial using the \(2\ \times\ 2\) table below. The vaccine was designed to eliminate a particular strain of the virus, called the “MN strain.” The trial consisted of 7 AIDS patients vaccinated with the new drug and 31 AIDS patients who were treated with a placebo (no vaccination). The table (saved in the HIV1 file) shows the number of patients who tested positive and negative for the MN strain in the trial follow-up period. a. Conduct a test to determine whether the vaccine is effective in treating the MN strain of HIV. Use \(\alpha\ =\ .05\). b. Are the assumptions for the test, part a, satisfied? What are the consequences if the assumptions are violated? c. In the case of ? \(2\ \times\ 2\) contingency table, R. A. Fisher (1935) developed a procedure for computing the exact p-value for the test (called Fisher’s exact test). The method uses the hypergeometric probability distribution (a discrete probability distribution not covered in Chapter 4). Consider the hypergeometric probability \(\frac{\left(\begin{array}{l} 7 \\ 2 \end{array}\right)\left(\begin{array}{l} 31 \\ 22 \end{array}\right)}{\left(\begin{array}{l} 38 \\ 24 \end{array}\right)}\) This represents the probability that 2 out of 7 vaccinated AIDS patients test positive and 22 out of 31 unvaccinated patients test positive (i.e., the probability of the table result given the null hypothesis of independence is true). Compute this probability (called the probability of the contingency table). d. Refer to part c. Two contingency tables (with the same marginal totals as the original table) that are more contradictory to the null hypothesis of independence than the observed table follow and are saved in the HIV2 and HIV3 files. First, explain why these tables provide more evidence to reject H0 than the original table; then compute the probability of each table using the hypergeometric formula. e. The p-value of Fisher’s exact test is the probability of observing a result at least as contradictory to the null hypothesis as the observed contingency table, given the same marginal totals. Sum the probabilities of parts c and d to obtain the p-value of Fisher’s exact test. (To verify your calculations, check the p-value at the bottom of the SPSS printout on the previous page.) Interpret this value in the context of the vaccine trial.

A random sample of 250 observations was classified according to the row and column categories shown in the table below. a. Do the data provide sufficient evidence to conclude that the rows and columns are dependent? Test using \(\alpha\ =\ .05\). b. Would the analysis change if the row totals were fixed before the data were collected? c. Do the assumptions required for the analysis to be valid differ according to whether the row (or column) totals are fixed? Explain. d. Convert the table entries to percentages by using each column total as a base and calculating each row response as a percentage of the corresponding column total. In addition, calculate the row totals and convert them to percentages of all 250 observations. e. Create a bar graph with row 1 percentage on the vertical axis against the column number on the horizontal axis. Draw horizontal lines corresponding to the row 1 percentages. Does the graph support the result of the test conducted in part a?

Location of major sports venues. There has been a recent trend for professional sports franchises in Major League Baseball (MLB), the National Football League (NFL), the National Basketball Association (NBA), and the National Hockey League (NHL) to build new stadiums and ballparks in urban, downtown venues. An article in Professional Geographer (Feb. 2000) investigated whether there has been a significant suburban-to-urban shift in the location of major sport facilities. In 1985, 40% of all major sport facilities were located downtown, 30% in central cities, and 30% in suburban areas. In contrast, of the 113 major sports franchises that existed in 1997, 58 were built downtown, 26 in central cities, and 29 in suburban areas. a. Describe the qualitative variable of interest in the study. Give the levels (categories) associated with the variable. b. Give the null hypothesis for a test to determine whether the proportions of major sports facilities in downtown, central city, and suburban areas in 1997 are the same as in 1985. c. If the null hypothesis of part b is true, how many of the 113 sports facilities in 1997 would you expect to be located in downtown, central city, and suburban areas, respectively? d. Find the value of the chi-square statistic for testing the null hypothesis of part b. e. Find the (approximate) p -value of the test, and give the appropriate conclusion in the words of the problem. Assume that \(\alpha\ =\ .05\).

“Made in the USA” survey. Refer to the Journal of Global Business (Spring 2002) study of what “Made in the USA” on product labels means to the typical consumer, Exercise 2.152 (p. 116). Recall that 106 shoppers participated in the survey. Their responses, given as a percentage of U.S. labor and materials in four categories, are summarized in the table. Suppose a consumer advocate group claims that half of all consumers believe that “Made in the USA” means “100%” of labor and materials are produced in the United States, one-fourth believe that " 75% to 99% " are produced in the United States, one-fifth believe that " 50% to 74% " are produced in the United States, and 5% believe that "less than 50% " are produced in the United States. a. Describe the qualitative variable of interest in the study. Give the levels (categories) associated with the variable. b. What are the values of \(p_1\), \(p_2\), \(p_3\), and \(p_4\), the probabilities associated with the four response categories hypothesized by the consumer advocate group? c. Give the null and alternative hypotheses for testing the consumer advocate group's claim. d. Compute the test statistic for testing the hypotheses, part c. e. Find the rejection region of the test at \(\alpha\ =\ .10\). f. State the conclusion in the words of the problem. g. Find and interpret a 90% confidence interval for the true proportion of consumers who believe "Made in the USA" means " 100% " of labor and materials are produced in the United States.

Dust plumes from farm equipment. Fugitive dust plumes generated by farm equipment can be hazardous to human health. In the Journal of Agricultural, Biological, and Environmental Sciences (Mar. 2001), environmental engineers developed a model for dust particle concentrations in plumes produced by a tractor operating in a wheat field. The tractor traveled along six parallel, equi-length paths in the field. A remote sensing instrument with a laser beam, placed at the edge of the field, measured the particulate matter in the dust every .5 seconds. Unfortunately, a few of the measurements were censored (i.e., higher than the signal level of the instrument). This usually occurred when the tractor was a short distance from the instrument’s laser beam. The table on the next page shows the number of censored measurements for each of the six tractor lines. a. Calculate and compare the sample proportion of censored measurements for the six tractor lines. b. Do the data provide sufficient evidence to indicate that the proportion of censored measurements differs for the six tractor lines? Test using \(\alpha\ =\ .01\). c. Comment on the practical versus statistical significance of the test.

Top Internet search engines. Nielsen/NetRatings is a global leader in Internet media and market research. In a recent year, the firm reported on the “search” shares (i.e., percentage of all Internet searches) for the most popular search engines available on the Web. Google accounted for 50% of all searches, Yahoo! for 22%, MSN for 11%, and all other search engines for 17%. Suppose that in a random sample of 1,000 recent Internet searches, 487 used Google, 245 used Yahoo!, 121 used MSN, and 147 used another search engine. a. Do the sample data disagree with the percentages reported by Nielsen/NetRatings? Test using \(\alpha\ =\ .05\). b. Find and interpret a 95% confidence interval for the percentage of all Internet searches that use the Google search engine.

Problem 44SE JAMA study of heart patients. The Journal of the American Medical Association (Apr. 18, 2001) published the results of a study of alcohol consumption in patients suffering from acute myocardial infarction (AMI). The patients were classified according to average number of alcoholic drinks per week and whether or not they had congestive heart failure. A summary of the results for 1,913 AMI patients is shown in the table. Source: Mukamal, K. J., et al. “Prior alcohol consumption and mortality following acute myocardial infarction,” Journal of the American Medical Association, Vol. 285, No. 15, April 18, 2001 (Table 1). a. Find the sample proportion of abstainers with congestive heart failure. b. Find the sample proportion of moderate drinkers (patients who have less than 7 drinks per week) with congestive heart failure. c. Find the sample proportion of heavy drinkers (patients who have 7 or more drinks per week) with congestive heart failure. d. Compare the sample proportions, parts a–c. Does it appear that the proportion of AMI patients with congestive heart failure depends on alcohol consumption? e. Give the null hypothesis for testing whether the proportion of AMI patients with congestive heart failure depends on alcohol consumption. f. Conduct the test, part e, using ? = .05. What do you conclude?

Problem 48SE Pig farm study. An article in Sociological Methods & Research (May 2001) analyzed the data presented in the table. A sample of 262 Kansas pig farmers was classified according to their education level (college or not) and size of their pig farm (number of pigs). Conduct a test to determine whether a pig farmer’s education level has an impact on the size of the pig farm. Use ? = .05 and support your answer with a graph. Source: Based on Agresti, A., & Liu, I. “Strategies for modeling a categorical variable allowing multiple category choices,” Sociological Methods & Research, Vol. 29, No. 4, May 2001 (Table 1).

Problem 47SE Ethical behavior of accountants. University of Louisville Professor Julia Karcher conducted an experiment to investigate the ethical behavior of accountants (Journal of Business Ethics, Vol. 15, 1996). She focused on auditor abilities to detect ethical problems that may not be obvious. Seventy auditors from Big-Six accounting firms were given a detailed case study that contained several problems, including tax evasion by the client. In 35 of the cases, the tax evasion issue was severe; in the other 35 cases, it was moderate. The auditors were asked to identify any problems they detected in the case. The following table summarizes the results for the ethical issue. Source: Karcher, J. “Auditors’ ability to discern the presence of ethical problems,” Journal of Business Ethics, Vol. 15(10), 1996, p. 1041 (Table V). Copyright © 1996 Springer. Reprinted with kind permission from Springer Science+Business Media B.V. a. Did the severity of the ethical issue influence whether the issue was identified or not by the auditors? Test using ? = .05. b. Suppose the left-hand column of the table contained the counts 35 and 0 instead of 27 and 8. Should the test of part a still be conducted? Explain. c. Keeping the sample size the same, change the numbers in the contingency table so that the answer you would get for the question posed in part a changes.

Survey on giving and volunteering. Refer to the study of charitable givers published in the National Tax Journal (Dec. 2001), Exercise 10.9 (p. 570). In addition to the 1,072 charitable givers who reported that their charitable contributions were motivated by tax considerations, another 1,693 givers reported no tax motivation, giving a total sample of 2,765 charitable givers. Of the 1,072 who were motivated by tax considerations, 691 itemized deductions on their income tax returns. Of the 1,693 who were not motivated by tax considerations, 794 itemized deductions. a. Consider the two categorical variables, tax motivation (yes or no) and itemize deductions (yes or no). Form a \(2\ \times\ 2\) contingency table for these variables. b. Compute the expected cell counts for the contingency table, part a. c. Compute the value of \(X^2\) for a test of independence. d. At \(\alpha\ =\ .05\), what inference can you make about whether the two variables, tax motivation and itemize deductions, are related for charitable givers? e. Create a bar graph that will visually support your conclusion in part d.

Problem 49SE Management system failures. Refer to the Process Safety Progress (Dec. 2004) and U.S. Chemical Safety and Hazard Investigation Board study of industrial accidents caused by management system failures, Exercise 2.146 (p. 115). The table below gives a breakdown of the root causes of a sample of 83 incidents. Are there significant differences in the percentage of incidents in the four cause categories? Test using ? = .05. Source: Blair, A. S. “Management system failures identified in incidents investigated by the U.S. Chemical Safety and Hazard Investigation Board,” Process Safety Progress, Vol. 23, No. 4, Dec. 2004, pp. 232–236 (Table 1). Copyright © 2004 by John Wiley & Sons. Reprinted with permission.

Colors of M&M’s candies. M&M’s plain chocolate candies come in six different colors: dark brown, yellow, red, orange, green, and blue. According to the manufacturer (Mars, Inc.), the color ratio in each large production batch is 30% brown, 20% yellow, 20% red, 10% orange, 10% green, and 10% blue. To test this claim, a professor at Carleton College (Minnesota) had students count the colors of M&M’s found in “fun size” bags of the candy. The results for 400 M&M’s sampled in a similar study are displayed in the next table. a. Assuming the manufacturer’s stated percentages are accurate, calculate the expected numbers falling into the six categories. b. Calculate the value of \(X^2\) for testing the manufacturer’s claim. c. Conduct a test to determine whether the true percentages of the colors produced differ from the manufacturer’s stated percentages. Use \(\alpha\ =\ .05\).

Performance of solder-joint inspectors. Westinghouse Electric Company has experimented with different means of evaluating the performance of solder-joint inspectors. One approach involves comparing an individual inspector’s classifications with those of the group of experts that comprise Westinghouse’s Work Standards Committee. In one experiment conducted by Westinghouse, 153 solder connections were evaluated by the committee, and 111 were classified as acceptable. An inspector evaluated the same 153 connections and classified 124 as acceptable. Of the items rejected by the inspector, the committee agreed with 19. a. Construct a contingency table that summarizes the classifications of the committee and the inspector. b. Based on a visual examination of the table you constructed in part a, does it appear that there is a relationship between the inspector’s classifications and the committee’s? Explain. (A graph of the percentage rejected by committee and inspector will aid your examination.) c. Conduct a chi-square test of independence for these data. Use \(\alpha=.05\). Carefully interpret the results of your test in the context of the problem.

History of corporate acquisitions. Refer to the Academy of Management Journal (Aug. 2008) investigation of the performance and timing of corporate acquisitions, Exercise 2.12 (p. 50). Data on the number of firms sampled and number that announced one or more acquisitions during the year from 1980 to 2000 are saved in the accompanying file. Suppose you want to determine if the proportion of firms with acquisitions differed annually from 1990 to 2000, that is, you want to determine if year and acquisition status were dependent from 1990 to 2000. a. Identify the two qualitative variables (and their respective categories) to be analyzed. b. Set up the null and alternative hypotheses for the test. c. Use the Minitab printout at the bottom of the page to conduct the test at \(\alpha\ =\ .5\).

Problem 52SE Multiple sclerosis drug. Interferons are proteins produced naturally by the human body that help fight infections and regulate the immune system. A drug developed from interferons, called Avonex, is now available for treating patients with multiple sclerosis (MS). In a clinical study, 85 MS patients received weekly injections of Avonex over a 2-year period. The number of exacerbations (i.e., flare-ups of symptoms) was recorded for each patient and is summarized in the accompanying table. For MS patients who take a placebo (no drug) over a similar two-week period, it is known from previous studies that 26% will experience no exacerbations, 30% one exacerbation, 11% two exacerbations, 14% three exacerbations, and 19% four or more exacerbations. a. Conduct a test to determine whether the exacerbation distribution of MS patients who take Avonex differs from the percentages reported for placebo patients. Test using ? = .05. b. Find a 95% confidence interval for the true proportion of Avonex MS patients who are exacerbation free during a 2-year period. c. Refer to part b. Is there evidence that Avonex patients are more likely to have no exacerbations than placebo patients? Explain.

“Fitness for use” of gasoline filters. Product or service quality is often defined as fitness for use. This means the product or service meets the customer’s needs. Generally speaking, fitness for use is based on five quality characteristics: technological (e.g., strength, hardness), psychological (taste, beauty), time-oriented (reliability), contractual (guarantee provisions), and ethical (courtesy, honesty). The quality of a service may involve all these characteristics, while the quality of a manufactured product generally depends on technological and time-oriented characteristics (Schroeder, Operations Management, 2008). After a barrage of customer complaints about poor quality, a manufacturer of gasoline filters for cars had its quality inspectors sample 600 filters—200 per work shift—and check for defects. The data in the table resulted. a. Do the data indicate that the quality of the filters being produced may be related to the shift producing the filter? Test using \(\alpha\ =\ .05.\) b. Estimate the proportion of defective filters produced by the first shift. Use a 95% confidence interval.

Problem 53SE Flight response of geese to helicopter traffic. Offshore oil drilling near an Alaskan estuary has led to increased air traffic—mostly large helicopters—in the area. The U.S. Fish and Wildlife Service commissioned a study to investigate the impact these helicopters have on the flocks of Pacific brant geese that inhabit the estuary in fall before migrating (Statistical Case Studies: A Collaboration between Academe and Industry, 1998). Two large helicopters were flown repeatedly over the estuary at different altitudes and lateral distances from the flock. The flight responses of the geese (recorded as “low” or “high”), altitude (hundreds of meters), and lateral distance (hundreds of meters) for each of Overflight Altitude Lateral Distance Flight Response 1 0.91 4.99 High 2 0.91 8.21 High 3 0.91 3.38 High 4 9.14 21.08 Low 5 1.52 6.6 High 6 0.91 3.38 High 7 3.05 0.16 High 8 6.1 3.38 High 9 3.05 6.6 High 10 12.19 6.6 High Source: Erickson, W., Nick, T., & Ward, D. “Investigating flight response of Pacific brant to helicopters at Izembek Lagoon, Alaska, by using logistic regression,” Statistical Case Studies: A Collaboration between Academe and Industry, Copyright © 1998 Society for Industrial and Applied Mathematics. Reprinted with permission. All rights reserved. the 464 helicopter overflights were recorded and are saved in the file. (The data for the first 10 overflights are shown in the preceding table.) a. The researchers categorized altitude as follows: less than 300 meters, 300–600 meters, and 600 or more meters. Summarize the data in the file by creating a contingency table for altitude category and flight response. b. Conduct a test to determine if flight response of the geese depends on altitude of the helicopter. Test using ? = .01. c. The researchers categorized lateral distance as follows: less than 1,000 meters, 1,000–2,000 meters, 2,000–3,000 meters, and 3,000 or more meters. Summarize the data in the file by creating a contingency table for lateral distance category and flight response. d. Conduct a test to determine if flight response of the geese depends on lateral distance of the helicopter from the flock. Test using ? = .01. e. The current Federal Aviation Authority (FAA) minimum altitude standard for flying over the estuary is 2,000 feet (approximately 610 meters). Based on the results, parts a–d, what changes to the FAA regulations do you recommend to minimize the effects to Pacific brant geese?

Software defects. The PROMISE Software Engineering Repository at the University of Ottawa provides researchers with data sets for building predictive software models. (See Exercise 2.160, p. 117.) Data on 498 modules of software code written in “C” language for a NASA spacecraft instrument are saved in the file. Recall that each module was analyzed for defects and classified as “true” if it contained defective code and “false” if not. One algorithm for predicting whether or not a module has defects is “essential complexity” (denoted EVG), where a module with at least 15 subflow graphs with D-structured primes is predicted to have a defect. When the method predicts a defect, the predicted EVG value is “yes”; otherwise, it is “no.” Would you recommend the essential complexity algorithm as a predictor of defective software modules? Explain.

Problem 55SE Goodness-of-fit test. A statistical analysis is to be done on a set of data consisting of 1,000 monthly salaries. The analysis requires the assumption that the sample was drawn from a normal distribution. A preliminary test, called the ?2 goodness-of-fit test , can be used to help determine whether it is reasonable to assume that the sample is from a normal distribution. Suppose the mean and standard deviation of the 1,000 salaries are hypothesized to be $1,200 and $200, respectively. Using the standard normal table, we can approximate the probability of a salary being in the intervals listed in the accompanying table. The third column represents the expected number of the 1,000 salaries to be found in each interval if the sample was drawn from a normal distribution with ? = $1,200 and ? = $200. Suppose the last column contains the actual observed frequencies in the sample. Large differences between the observed and expected frequencies cast doubt on the normality assumption. a. Compute the ?2 statistic on the basis of the observed and expected frequencies. ________________ b. Find the tabulated ?2 value when ? = .05 and there are five degrees of freedom. (There are k - 1 = 5 df associated with this ?2 statistic.) ________________ c. On the basis of the ?2 statistic and the tabulated ?2 value, is there evidence that the salary distribution is nonnormal? ________________ d. Find the approximate observed significance level for the test in part c.