Chapter 9: Introduction to Hypothesis Testing

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424 CHAPTER 9 • INTRODUCTION TO HYPOTHESIS TESTING American workers. Calculate the probability that this would be the case. (Hint: Review the procedure concerning the sample mean and perform the analogous procedure for a proportion.) b. Conduct the procedure to determine if the proportion of workers who wouldn’t object to the company monitoring their Internet use after they were informed is more than 50%. Use a significance level of 0.05. 9-91. General Motors Corp., the world’s largest automaker, has been the global industry sales leader since 1931. Founded in 1908, GM today employs about 317,000 people around the world. As do most large corporations, it offers an extensive retirement program. According to USA Today (Moneyline, August 5, 2005), during 2004 the average balance in workers 401(k) accounts rose 10%, to $61,000. To determine if GM’s workers are keeping pace with the rest of the nation’s workforce, a sample of 55 might be obtained and produce a sample average of $61,834.12. a. If the standard deviation for the amount in workers’ accounts is $1,734.23, determine if GM’s workers’ average balance in 401(k) accounts is keeping pace. Use a significance level of 0.025. b. Determine the largest plausible average balance in the GM workers’ 401(k) accounts in which you could have 90% confidence. Computer Database Exercises 9-92. The Haines Lumber Company makes plywood for the furniture industry. One product it makes is 3 – 4 -inch oak veneer panels. It is very important that the panels conform to specifications. One specification calls for the panels to be made to an average thickness of 0.75 inch. Each hour, 5 panels are selected at random and measured. After 20 hours a total of 100 panels have been measured. The thickness measures are in a file called Haines. a. Formulate the appropriate null and alternative hypotheses relative to the thickness specification. b. Based on the sample data, what should the company conclude about the status of its product meeting the thickness specification? Test at a significance level of 0.01. Discuss your results in a report to the production manager. 9-93. The Wilson Company uses a great deal of water in the process of making industrial milling equipment. To comply with the federal clean water laws, it has a water purification system that all wastewater goes through before being discharged into a settling pond on the company’s property. To determine whether the company is complying with the federal requirements, sample measures are taken every so often. One requirement is that the average pH level not exceed 7.4. A sample of 95 pH measures has been taken. The data for these measures are shown in a file called Wilson Water. a. Considering the requirement for pH level, state the appropriate null and alternative hypotheses. Discuss why it is appropriate to form the hypotheses with the federal standard as the alternative hypothesis. b. Based on the sample data of pH level, what should the company conclude about its current status on meeting the federal requirement? Test the hypothesis at the 0.05 level. Discuss your results in a memo to the company’s environmental relations manager. 9-94. The AJ Fitness Center has surveyed 1,214 of its customers. Of particular interest is whether over 60% of the customers who express overall service satisfaction with the club (represented by codes 4 or 5) are female. If this is not the case, the promotions director feels she must initiate new exercise programs that are designed specifically for women. Should the promotions director initiate the new exercise programs? Support your answer with the relevant hypothesis test utilizing a p-value to perform the test. The data are found in a data file called AJ Fitness (0.05). 9-95. At the annual meeting of the Golf Equipment Manufacturer’s Association, a speaker made the claim that over 30% of all golf clubs being used by nonprofessional United States Golf Association members are “knock-offs.” These “knock-offs” are clubs that look very much like the more expensive originals, such as Big Bertha drivers, but are actually nonauthorized copies that are sold at a very reduced rate. This claim prompted the association to conduct a study to see if the problem was as big as the speaker said. A random sample of 400 golfers was selected from the USGA membership ranks. The players were called and asked to indicate the brand of clubs that they used and several other questions. Out of the 400 golfers, data were collected from 294 of them. Based on the response to club brand, a determination was made whether the club was “original” or a “copy.” The data are in a file called Golf Survey. a. Based on the sample data, what conclusion should be reached if the hypothesis is tested at a significance level of 0.05? Show the decision rule. b. Determine whether a Type I or Type II error for this hypothesis test would be more severe. Given your determination, would you advocate raising or lowering the significance level for this test? Explain your reasoning. c. Confirm that the sample proportion’s distribution can be approximated by a normal distribution.
CHAPTER 9 • INTRODUCTION TO HYPOTHESIS TESTING 425 d. Based on the sample data, what should the USGA conclude about the use of “knock-off” clubs by the high-handicap golfers? Is the official’s statement justified? 9-96. The Inland Empire Food Store Company has stated in its advertising that the average shopper will save more than $5.00 per week by shopping at Inland stores. A consumer group has decided to test this assertion by sampling 50 shoppers who currently shop at other stores. It selects the customers and then notes each item purchased at their regular store. These same items are then priced at the Inland store and the total bill is compared. The data in the file Inland Foods reflect savings at Inland for the 50 shoppers. Note that those cases where the bill was higher at Inland are marked with a minus sign. a. Set up the appropriate null and alternative hypotheses to test Inland’s claim. b. Using a significance level of 0.05, develop the decision rule and test the hypothesis. Can Inland Empire support its advertising claim? c. Which type of hypothesis error would the consumer group be most interested in controlling? Which type of hypothesis error would the company be most interested in controlling? Explain your reasoning. 9-97. The Cell Tone Company sells cellular phones and airtime in several northwestern states. At a recent meeting, the marketing manager stated that the average age of its customers is under 40. This came up in conjunction with a proposed advertising plan that is to be directed toward a young audience. Before actually completing the advertising plan, Cell Tone decided to randomly sample customers. Among the questions asked in the survey of 50 customers in the Jacksonville, Florida, area was the customer’s age. The data are available in a data file called Cell Phone Survey. a. Based on the statement made by the marketing manager, formulate the appropriate null and alternative hypotheses. b. The marketing manager must support his statement concerning average customer age in an upcoming board meeting. Using a significance level of 0.10, provide this support for the marketing manager. c. Consider the result of the hypothesis test you conducted in part b. Which of the two types of hypothesis test errors could you have committed? How could you discover if you had, indeed, made this error? d. Calculate the critical value, x. e. Use the critical value, x, to determine the p-value and conduct the test using the p-value approach. f. Note that the sample data list the customer’s age to the nearest year. (1) If we denote a randomly selected customer’s age (to the nearest year) as x i , is x i a continuous or discrete random variable? (2) Is it possible that x i has a normal distribution? Consider your answers to (1) and (2) and the fact that x must have a normal distribution to facilitate the calculation in part b. Does this mean that the calculation you have performed in part b is inappropriate? Explain your answer. 9-98. MBNA offers personal and business credit cards, loans, and savings products. It was bought by Bank of America in June 2005. One of the selling points for MBNA was its position relative to the rest of the credit card industry. MBNA’s customers’ average annual spending per active account before the purchase was $6,920. To demonstrate its relative position in the industry, MBNA’s CFO, H. Vernon Wright, might authorize a survey producing the following data on the annual spending, to the nearest dollar, of accounts in the industry: 3,680 6,255 6,777 7,412 4,902 5,522 5,190 7,976 4,116 3,949 6,814 2,264 4,991 5,353 5,914 5,828 6,059 6,354 6,193 5,648 6,117 7,315 6,458 4,973 6,554 1,926 4,395 5,341 4,921 6,268 4,061 4,777 5,876 5,984 3,381 5,441 4,268 7,657 6,449 4,821 This sample is contained in the CD-ROM file labeled ASpending. a. Conduct a hypothesis test to determine if MBNA has larger average annual spending per active account than the rest of the credit card industry. Use a p-value approach and a significance level of 0.025. b. If the industry’s annual spending per active account was normally distributed with a mean of $5,560 and a standard deviation of $1,140, determine the probability that a randomly chosen account would have an annual spending larger than MBNA’s. 9-99. TOMRA Systems ASA is a Norwegian company that manufactures reverse vending machines (RVMs). In most cases, RVMs are used in markets that have deposits on beverage containers, offering an efficient and convenient method of identifying the deposit amount of each container returned and providing a refund to the customer. Prices for such machines range from about $9,000 for single-container machines to about $35,000 for higher-volume, multi-container (can, plastic, glass) machines. To pay for a single-container machine in one year, an average monthly income would have to be at least $750. The following
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Chapter 9: Introduction to Hypothesis Testing

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