Chapter 9: Introduction to Hypothesis Testing

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404 CHAPTER 9 • INTRODUCTION TO HYPOTHESIS TESTING Step 7 Draw a conclusion. Based on the sample data, the athletic director does not have sufficient evidence to conclude that more than 10% of the season ticket holders will cancel their ticket orders. 9-2: Exercises Skill Development 9-23. Determine the appropriate critical value(s) for each of the following tests concerning the population proportion: a. upper-tailed test: 0.025, n 48 b. lower-tailed test: 0.05, n 30 c. two-tailed test: 0.02, n 129 d. two-tailed test; 0.10, n 36 9-24. For the following hypothesis test: H 0 : 0.40 H A : 0.40 0.01 with n 64 and p 0.42, state a. the decision rule in terms of the critical value of the test statistic. b. the calculated value of the test statistic. c. the conclusion. 9-25. For the following hypothesis test: H 0 : 0.75 H A : 0.75 0.025 with n 100 and p 0.66, state a. the decision rule in terms of the critical value of the test statistic. b. the calculated value of the test statistic. c. the conclusion. 9-26. Calculate the z-test statistic for a hypothesis test in which the null hypothesis states that the population proportion, , equals 0.40 if the following sample information is present: n 150, x 30 9-27. Given the following null and alternative hypotheses: H 0 : 0.60 H A : 0.60 test the hypothesis using 0.01 assuming that a sample of n 200 yielded x 105 items with the desired attribute. 9-28. A test of hypothesis has the following hypotheses: H 0 : 0.45 H A : 0.45 For a sample size of 30, and a sample proportion of 0.55, a. for an 0.025, determine the critical value. b. calculate the numerical value of the test statistic. c. state the test’s conclusion. d. determine the p-value. 9-29. A sample of size 25 was obtained to test the hypotheses H 0 : 0.30 H A : 0.30 Calculate the p-value for each of the following sample results: a. p 0.12 b. p 0.35 c. p 0.42 d. p 0.5 Business Applications 9-30. A major issue facing many states is whether to legalize casino gambling. Suppose the governor of one state believes that more than 55% of the state’s registered voters would favor some form of legal casino gambling. However, before backing a proposal to allow such gambling, the governor has instructed his aides to conduct a statistical test on the issue. To do this, the aides have hired a consulting firm to survey a simple random sample of 300 voters in the state. Of these 300 voters, 175 actually favored legalized gambling. a. State the appropriate null and alternative hypotheses. b. Assuming that a significance level of 0.05 is used, what conclusion should the governor reach based upon these sample data? Discuss. 9-31. An issue that faces individuals investing for retirement is allocating assets among different investment choices. Suppose a study conducted 10 years ago showed that 65% of investors preferred stocks to real estate as an investment. In a recent random sample of 900 investors, 360 preferred real estate to stocks. Is this new data sufficient to allow you to conclude that the proportion of investors preferring
CHAPTER 9 • INTRODUCTION TO HYPOTHESIS TESTING 405 stocks to real estate has declined from 10 years ago? Conduct your analysis at the 0.02 level of significance. 9-32. A Washington Post–ABC News poll taken in March 2005 found that 72% of people are concerned about the possibility that their personal records could be stolen over the Internet (Salina Journal, June 13, 2005). If a random sample of 300 college students at a Midwestern university were taken and 228 of them were concerned about the possibility that their personal records could be stolen over the Internet, could you conclude at the 0.025 level of significance that a higher proportion of the university’s college students are concerned about Internet theft than the public at large? Report the p-value for this test. 9-33. An April 2004 article published by the Detroit Free Press entitled “Assistance: IRS Help Centers Give the Wrong Information” discusses the propensity of IRS staff employees to give wrong tax information to taxpayers who call with questions. IRS Inspector General Pamela Gardiner told a Senate subcommittee that “. . . the IRS employees at 400 taxpayer assistance centers nationwide encountered 8.5 million taxpayers face-to-face last year. The problem: When inspector general auditors posing as taxpayers asked them to answer tax questions, the answers were right 69% of the time” (see www.freep.com/money/business/taxhel12_ 20040412.htm). Suppose an independent commission was formed to test whether the 0.69 accuracy rate is correct or whether it is actually higher or lower. The commission has randomly selected n 180 tax returns that were completed by IRS assistance employees and found that 105 of the returns were accurately completed. a. State the appropriate null and alternative hypotheses. b. Using an 0.05 level, based on the sample data, what conclusion should be reached about the IRS rate of correct tax returns? Discuss your results. 9-34. A July 13, 2005 article on the front page of The Wall Street Journal entitled “As Identity Theft Moves Online, Crime Rings Mimic Big Business” states that 39% of the consumer scam complaints by American consumers is about identity theft. Suppose a random sample of 90 complaints is obtained. Of these complaints, 40 were regarding identity theft. Based on these sample data, what conclusion should be reached about the statement made in The Wall Street Journal? (Test using 0.10.) 9-35. In July 2005, an Associated Press article written by Eileen Powell entitled “Credit Card Payments Going Up” described a recent change in credit card policies. Under pressure from federal regulators, credit card issuers have started to raise the minimum payment that consumers are required to pay on outstanding credit card balances. Suppose a claim is made that more than 40% of all credit card holders pay the minimum payment. To test this claim, a random sample of payments made by credit card customers was collected. The sample contained data for 400 customers, of which 174 paid the minimum payment. a. State the appropriate null and alternative hypotheses. b. Based on the sample data, test the null hypothesis using an alpha level equal to 0.05. Discuss the results of the test. 9-36. The practice of “phishing,” or using the Internet to pilfer personal information, has become an increasing concern, not only for individual computer users but also for online retailers and financial institutions. The Wall Street Journal (June 23, 2005) reported 28% of people who bank online have cut back on their Internet use. The North Central Educators Credit Union instituted an extensive online security and educational program six months ago in an effort to combat phishing before the problem became extreme. The credit union’s managers are certain that while Internet use may be down, it is much less than 28% of its customers. In fact, they are convinced that at most 10% of their customers have reduced their Internet banking transactions. The credit union’s IT department analyzed 200 randomly selected accounts and determined that 24 indicated Internet banking had either been reduced or stopped entirely. a. State the appropriate null and alternative hypotheses for this situation. b. Using 0.05 and the p-value approach, indicate whether the sample data support the managers’ contention. 9-37. CEO Chris Foreman of Pacific Theaters Exhibition Corp. is taking steps to reverse the decline in movie attendance. Moviegoers’ comfort is one of the issues facing theaters. Pacific Theaters has begun offering assigned seating, no in-theater advertising, and a live announcer who introduces films and warns patrons to turn off cell phones. Despite such efforts, an Associated Press/America Online News poll of 1,000 adults (USA Today, “Movie maladies,” June 23, 2005) discovered that 730 of those surveyed preferred seeing movies in their homes. a. Using a significance level of 0.025, conduct a statistical procedure to determine if the Associated Press/America Online News poll indicates that more than 70% of adults prefer seeing movies in their homes. Use a p-value approach.
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Chapter 9: Introduction to Hypothesis Testing

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