Chapter 9: Introduction to Hypothesis Testing

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406 CHAPTER 9 • INTRODUCTION TO HYPOTHESIS TESTING b. Express a Type II error in the context of this exercise’s scenario. 9-38. Harris Interactive Inc., the 15th largest market research firm in the world, is a Rochester, New York-based company. In 2005, one of their surveys indicated that 26% of women have had experience with a Global Positioning System device. The survey (USA Today, Snapshots, July 12, 2005) indicated that 36% of the men surveyed used a Global Positioning System device. a. If the survey was based upon a sample size of 290 men, does this data indicate that the proportion of men is the same as the proportion of women who have had experience with a Global Positioning System device? Use a significance level of 0.05. b. Obtain the p-value for the test indicated in part a. 9-39. A large number of complaints have been received in the past six months regarding airlines losing fliers’ baggage. The airlines claim the problem is nowhere near as great as the newspaper articles have indicated. In fact, one airline spokesman claimed that less than 1% of all bags fail to arrive at the destination with the passenger. To test this claim, 800 bags were randomly selected at various airports in the United States when they were checked with this airline. Of these, 6 failed to reach the destination when the passenger (owner) arrived. a. Is this sufficient evidence to support the airline spokesman’s claim? Test using a significance level of 0.05. Discuss. b. Estimate the proportion of bags that fail to arrive at the proper destination using a technique for which 95% confidence applies. Computer Database Exercises 9-40. According to the Employee Benefit Research Institute (www.ebri.org), 34% of workers between the ages of 35 and 44 owned a 401(k)-type retirement plan in 2002. Suppose a recent survey was conducted by the Atlanta Chamber of Commerce to determine the participation rate of 35–44-year-old working adults in the Atlanta metropolitan area who owned 401(k)-type retirement plans. The results of the survey can be found in the file Atlanta Retirement. Based on the survey results, can the Atlanta Chamber of Commerce conclude that the participation rate for 35–44-year-old working adults in Atlanta is higher than the 2002 national rate? Conduct your analysis at the 0.025 level of significance. 9-41. A survey by the Pew Internet & American Life Project conducted between January 13 and February 9, 2005 (http://www.pewinternet.org/ pdfs/PIP_Spam_Ap05.pdf) found that 21% of workers with an e-mail account at work say that they are getting more spam than a year ago. Suppose a large multinational company, after implementing a policy to combat spam, asked 198 randomly selected employees with e-mail accounts at work whether they are receiving more spam today than they did a year ago. The results of the survey are in the file Spam. At the 0.025 level of significance, can the company conclude that a smaller percentage of its employees is receiving more spam than a year ago than that found by the Pew study? 9-42. A study by the Investment Company Institute (ICI) in 2004, which randomly surveyed 3,500 households and drew upon information from the Internal Revenue Service, found that 72% of households have conducted at least one IRA rollover from an employer-sponsored retirement plan (www.financial-planning.com). Suppose a recent random sample of 90 households in the greater Miami area was taken and respondents were asked whether they had ever funded an IRA account with a rollover from an employersponsored retirement plan. The results are in the file Miami Rollover. Based on the sample data, can you conclude at the 0.10 level of significance that the proportion of households in the greater Miami area that have funded an IRA with a rollover is different from the proportion for all households reported in the ICI study? 9-43. Cell phones are becoming an integral part of our daily lives. Commissioned by Motorola, a new behavioral study took researchers to nine cities worldwide from New York to London. Using a combination of personal interviews, field studies, and observation, the study identified a variety of behaviors that demonstrate the dramatic impact cell phones are having on the way people interact. The study found cell phones give people a newfound personal power, enabling unprecedented mobility and allowing them to conduct their business on the go. Interesting enough, gender differences can be found in phone use. Women see their cell phone as a means of expression and social communication, while males tend to use it as an interactive toy. A cell phone industry spokesman stated that half of all cell phones in use are registered to females. a. State the appropriate null and alternative hypotheses for testing the industry claim. b. Based on a random sample of cell phone owners shown in the data file called Cell Phone Survey, test the null hypothesis. (Use 0.05.) 9-44. The Electronic Controls Company (ECCO) is one of the largest makers of backup alarms in the world. Backup alarms are the safety devices that emit a high-pitched beeping sound when a truck,
CHAPTER 9 • INTRODUCTION TO HYPOTHESIS TESTING 407 forklift, or other equipment is operated in reverse. ECCO is well known in the industry for its high quality and excellent customer service, but some products are returned under warranty due to quality problems. ECCO’s operations manager recently stated that less than half of the warranty returns are wiring-related problems. To verify if she is correct, a company intern was asked to select a random sample of warranty returns and determine the proportion that were returned due to wiring problems. The data the intern collected are shown in the data file called ECCO. a. State the appropriate null and alternative hypotheses. b. Conduct the hypothesis test using 0.02 and provide an interpretation of the result of the hypothesis test in terms of the operation manager’s claim. 9-45. Joseph-Armand Bombardier founded the company in the 1930s that is now known as Seadoo in Canada. His initial invention of the snowmobile in 1937 led the way to what is now a 7,600-employee, worldwide company specializing in both snow and water sports vehicles. The company stresses high quality in both manufacturing and dealer service. Suppose that the company standard for customer satisfaction is 95% “highly satisfied.” Company managers recently completed a customer survey of 700 customers from around the world. The responses to the question, “What is your overall level of satisfaction with Seadoo?” are provided in the file called Seadoo. a. State the appropriate null and alternative hypotheses to be tested. b. Using an alpha level of 0.05, conduct the hypothesis test and discuss the conclusions. 9.3 Type II Errors Sections 9.1 and 9.2 provided several examples that illustrated how hypotheses and decision rules for tests of the population mean or population proportion are formulated. In these examples, we determined the critical values by first specifying the significance level, alpha: the maximum allowable probability of committing a Type I error. As we indicated, if the cost of committing a Type I error is high, the decision maker will want to specify a small significance level. This logic provides a basis for establishing the critical value for the hypothesis test. However, it ignores the possibility of committing a Type II error. Recall that a Type II error occurs if a false null hypothesis is “accepted.” The probability of a Type II error is given by the symbol , the Greek letter beta. We discussed in Section 9.1 that and are inversely related. That is, if we make smaller, will increase. However, the two are not proportional. A case in point: Cutting in half will not necessarily double . CHAPTER OUTCOME #5 Business Application Calculating Beta Once has been specified for a hypothesis test involving a particular sample size, cannot also be specified. Rather, the value is fixed, and all the decision maker can do is calculate it. However, is not a single value. Because a Type II error occurs when a false null hypothesis is “accepted” (refer to Figure 9.1), there is a value for each possible population value for which the null hypothesis is false. To calculate beta, we must first specify a “what-if” value for the true population parameter. Then, is computed conditional on that parameter being true. Keep in mind that is computed before the sample is taken, so its value is not dependent on the sample outcome. For instance, if the null hypothesis is that the mean income for a population is equal to or greater than $30,000, then could be calculated for any value of less than $30,000. We would get a different for each value of . An application will help clarify this concept. AMERICAN LIGHTING COMPANY The American Lighting Company has developed a new light bulb to last more than 700 hours on average. If a hypothesis test could confirm this, the company would use the “greater than 700 hour” statement in its advertising. The null and alternative hypotheses are H 0 : 700 hours H A : 700 hours (research hypothesis)
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Chapter 9: Introduction to Hypothesis Testing

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