a. Use the p-value approach.
b. Repeat the test using the critical value approach.
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12.2 Suppose we have a multinomial population with four categories: A, B, C, and D. The null hypothesis is that the proportion of items is the same in every category. The null hypothesis is...A sample of size 300 yielded the following results....Use α = .05 to determine whether H0 should be rejected. What is the p-value?
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12.3 During the first 13 weeks of the television season, the Saturday evening 8:00 p.m. to 9:00 p.m. audience proportions were recorded as ABC 29%, CBS 28%, NBC 25%, and independents 18%. A sample of 300 homes two weeks after a Saturday night schedule revision yielded the following viewing audience data: ABC 95 homes, CBS 70 homes, NBC 89 homes, and independents 46 homes. Test with α = .05 to determine whether the viewing audience proportions changed.
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12.4 M&M/MARS makers of M&M® Chocolate Candies, conducted a national poll in which consumers indicated their preference for colors. In the brochure “Colors,” made available by M&M/MARS Consumer Affairs, the traditional distribution of colors for the plain candies is as follows:...In a follow-up study, 1-pound bags were used to determine whether the reported percentages were valid. The following results were obtained for a sample of 506 plain candies....Use α = .05 to determine whether these data support the percentages reported by the company.
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12.5 Where do women most often buy casual clothing? Data from the U.S. Shopper Database provided the following percentages for women shopping at each of the various outlets (The Wall Street Journal, January 28, 2004)....The other category included outlets such as Target, Kmart, and Sears as well as numerous smaller specialty outlets. No individual outlet in this group accounted for more than 5% of the women shoppers. A recent survey using a sample of 140 women shoppers in Atlanta, Georgia, found 42 Wal-Mart, 20 traditional department store, 8 J.C. Penney, 10 Kohl’s, 21 mail order, and 39 other outlet shoppers. Does this sample suggest that women shoppers in Atlanta differ from the shopping preferences expressed in the U.S. Shopper Database? What is the p-value? Use a = .05. What is your conclusion?
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12.6 The American Bankers Association collects data on the use of credit cards, debit cards, personal checks, and cash when consumers pay for in-store purchases (The Wall Street Journal, December 16, 2003). In 1999, the following usages were reported....A sample taken in 2003 found that for 220 in-stores purchases, 46 used a credit card, 67 used a debit card, 33 used a personal check, and 74 used cash.
a. At a = .01, can we conclude that a change occurred in how customers paid for in-store purchases over the four-year period from 1999 to 2003? What is the p-value?
b. Compute the percentage of use for each method of payment using the 2003 sample data. What appears to have been the major change or changes over the four-year period?
c. In 2003, what percentage of payments was made using plastic (credit card or debit card)?
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12.7 The Wall Street Journal’s Shareholder Scoreboard tracks the performance of 1000 major U.S. companies (The Wall Street Journal, March 10, 2003). The performance of each company is rated based on the annual total return, including stock price changes and the reinvestment of dividends. Ratings are assigned by dividing all 1000 companies into five groups from A (top 20%), B (next 20%), to E (bottom 20%). Shown here are the one-year ratings for a sample of 60 of the largest companies. Do the largest companies differ in performance from the performance of the 1000 companies in the Shareholder Scoreboard? Use α = .05....
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12.8 How well do airline companies serve their customers? A study showed the following customer ratings: 3% excellent, 28% good, 45% fair, and 24% poor (Business Week, September 11, 2000). In a follow-up study of service by telephone companies, assume that a sample of 400 adults found the following customer ratings: 24 excellent, 124 good, 172 fair, and 80 poor. Is the distribution of the customer ratings for telephone companies different from the distribution of customer ratings for airline companies? Test with α = .01. What is your conclusion?
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12.9 The following 2 × 3 contingency table contains observed frequencies for a sample of 200. Test for independence of the row and column variables using the χ2 test with α = .05....
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12.10 The following 3 × 3 contingency table contains observed frequencies for a sample of 240. Test for independence of the row and column variables using the χ2 test with α = .05....
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12.11 One of the questions on the Business Week Subscriber Study was, “In the past 12 months, when traveling for business, what type of airline ticket did you purchase most often? ” The data obtained are shown in the following contingency table....Use α = .05 and test for the independence of type of flight and type of ticket. What is your conclusion?
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12.12 Visa Card USA studied how frequently consumers of various age groups use plastic cards (debit and credit cards) when making purchases (Associated Press, January 16, 2006). Sample data for 300 customers shows the use of plastic cards by four age groups....
a. Test for the independence between method of payment and age group. What is the p-value? Using α = .05, what is your conclusion?
b. If method of payment and age group are not independent, what observation can you make about how different age groups use plastic to make purchases?
c. What implications does this study have for companies such as Visa, MasterCard, and Discover?
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12.13 With double-digit annual percentage increases in the cost of health insurance, more and more workers are likely to lack health insurance coverage (USA Today, January 23, 2004). The following sample data provide a comparison of workers with and without health insurance coverage for small, medium, and large companies. For the purposes of this study, small companies are companies that have fewer than 100 employees. Medium companies have 100 to 999 employees, and large companies have 1000 or more employees. Sample data are reported for 50 employees of small companies, 75 employees of medium companies, and 100 employees of large companies....
a. Conduct a test of independence to determine whether employee health insurance coverage is independent of the size of the company. Use α = .05. What is the p-value, and what is your conclusion?
b. The USA Today article indicated employees of small companies are more likely to lack health insurance coverage. Use percentages based on the preceding data to support this conclusion.
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12.14
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12.15 Flight Stats, Inc., collects data on the number of flights scheduled and the number of flights flown at major airports throughout the United States. Flight Stats data showed 56% of flights scheduled at Newark, La Guardia, and Kennedy airports were flown during a three-day snowstorm (The Wall Street Journal, February 21, 2006). All airlines say they always operate within set safety parameters—if conditions are too poor, they don’t fly. The following data show a sample of 400 scheduled flights during the snowstorm....Use the chi-square test of independence with a .05 level of significance to analyze the data. What is your conclusion? Do you have a preference for which airline you would choose to fly during similar snowstorm conditions? Explain.
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12.16
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12.17 The National Sleep Foundation used a survey to determine whether hours of sleeping per night are independent of age (Newsweek, January 19, 2004). The following table shows the hours of sleep on weeknights for a sample of individuals age 49 and younger and for a sample of individuals age 50 and older....
a. Conduct a test of independence to determine whether the hours of sleep on weeknights are independent of age. Use α = .05. What is the p-value, and what is your conclusion?
b. What is your estimate of the percentage of people who sleep fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 or more hours on weeknights?
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12.18
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12.19
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12.20 Data on the number of occurrences per time period and observed frequencies follow. Use α = .05 and the goodness of fit test to see whether the data fit a Poisson distribution....
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12.21 The following data are believed to have come from a normal distribution. Use the goodness of fit test and α = .05 to test this claim....
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12.22 The number of automobile accidents per day in a particular city is believed to have a Poisson distribution. A sample of 80 days during the past year gives the following data. Do these data support the belief that the number of accidents per day has a Poisson distribution? Use α = .05....
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12.23 The number of incoming phone calls at a company switchboard during one-minute intervals is believed to have a Poisson distribution. Use α = .10 and the following data to test the assumption that the incoming phone calls follow a Poisson distribution....
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12.24 The weekly demand for a product is believed to be normally distributed. Use a goodness of fit test and the following data to test this assumption. Use α = .10. The sample mean is 24.5 and the sample standard deviation is 3....
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12.25 Use α = .01 and conduct a goodness of fit test to see whether the following sample appears to have been selected from a normal distribution....After you complete the goodness of fit calculations, construct a histogram of the data. Does the histogram representation support the conclusion reached with the goodness of fit test? (Note: x = 71 and s = 17.)
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12.26 In setting sales quotas, the marketing manager makes the assumption that order potentials are the same for each of four sales territories. A sample of 200 sales follows. Should the manager’s assumption be rejected? Use a = .05....
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12.27 Seven percent of mutual fund investors rate corporate stocks “very safe,” 58% rate them “somewhat safe,” 24% rate them “not very safe,” 4% rate them “not at all safe,” and 7% are “not sure.” A Business Week/Harris poll asked 529 mutual fund investors how they would rate corporate bonds on safety. The responses are as follows....Do mutual fund investors’ attitudes toward corporate bonds differ from their attitudes toward corporate stocks? Support your conclusion with a statistical test. Use α = .01.
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12.28 Since 2000, the Toyota Camry, Honda Accord, and Ford Taurus have been the three bestselling passenger cars in the United States. Based on the 2003 sales data, the market shares among the top three are as follows: Toyota Camry 37%, Honda Accord 34%, and Ford Taurus 29% (The World Almanac, 2004). Assume a sample of 1200 sales of passenger cars during the first quarter of 2004 shows the following....Can these data be used to conclude that the market shares among the top three passenger cars have changed during the first quarter of 2004? What is the p-value? Use a .05 level of significance. What is your conclusion?
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12.29 A regional transit authority is concerned about the number of riders on one of its bus routes. In setting up the route, the assumption is that the number of riders is the same on every day from Monday through Friday. Using the following data, test with α = .05 to determine whether the transit authority’s assumption is correct....
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12.30 The results of Computerworld’s Annual Job Satisfaction Survey showed that 28% of information systems (IS) managers are very satisfied with their job, 46% are somewhat satisfied, 12% are neither satisfied nor dissatisfied, 10% are somewhat dissatisfied, and 4% are very dissatisfied. Suppose that a sample of 500 computer programmers yielded the following results....Use α = .05 and test to determine whether the job satisfaction for computer programmers is different from the job satisfaction for IS managers.
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12.31 A sample of parts provided the following contingency table data on part quality by production shift....Use α = .05 and test the hypothesis that part quality is independent of the production shift. What is your conclusion?
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12.32 The Wall Street Journal Subscriber Study showed data on the employment status of subscribers. Sample results corresponding to subscribers of the eastern and western editions are shown here....Use α = .05 and test the hypothesis that employment status is independent of the region. What is your conclusion?
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12.33 A lending institution supplied the following data on loan approvals by four loan officers. Use α = .05 and test to determine whether the loan approval decision is independent of the loan officer reviewing the loan application....
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12.34
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12.35 Barona Research Group collected data showing church attendance by age group (USA Today, November 20, 2003). Use the sample data to determine whether attending church is independent of age. Use a .05 level of significance. What is your conclusion? What conclusion can you draw about church attendance as individuals grow older?...
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12.36 The following data were collected on the number of emergency ambulance calls for an urban county and a rural county in Virginia....Conduct a test for independence using α = .05. What is your conclusion?
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12.37 A random sample of final examination grades for a college course follows....Use α = .05 and test to determine whether a normal distribution should be rejected as being representative of the population’s distribution of grades.
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12.38 The office occupancy rates were reported for four California metropolitan areas. Do the following data suggest that the office vacancies were independent of metropolitan area? Use a .05 level of significance. What is your conclusion?...
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12.39 A salesperson makes four calls per day. A sample of 100 days gives the following frequencies of sales volumes....Records show sales are made to 30% of all sales calls. Assuming independent sales calls, the number of sales per day should follow a binomial distribution. The binomial probability function presented in Chapter 5 is...For this exercise, assume that the population has a binomial distribution with n = 4, p = .30, and x = 0, 1, 2, 3, and 4.
a. Compute the expected frequencies for x = 0, 1, 2, 3, and 4 by using the binomial probability function. Combine categories if necessary to satisfy the requirement that the expected frequency is five or more for all categories.
b. Use the goodness of fit test to determine whether the assumption of a binomial distribution should be rejected. Use α = .05. Because no parameters of the binomial distribution were estimated from the sample data, the degrees of freedom are k – 1 when k is the number of categories.
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