Problem Set $8

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Problem Set #8 (Chapter 9) 8. Production Operating Costs. Suppose a new production method will be implemented if a hypothesis test supports the conclusion that the new method reduces the mean operating cost per hour. LO 1, 3 a. State the appropriate null and alternative hypotheses if the mean cost for the current production method is $220 per hour. b. What is the Type I error in this situation? What are the consequences of making this error? c. What is the Type Il error in this situation? What are the consequences of making this error? 15. Federal Tax Returns. According to the Internal Revenue Service (IRS), individuals filing federal income tax returns prior to March 31 received an average refund of $1056 in 2018. Consider the population of “last-minute” filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15).101,2,4 a. A researcher suggests that a reason individuals wait until the last five days is that on average these individuals receive lower refunds than do early filers. Develop appropriate hypotheses such that rejection of Hy will support the researcher’s contention. b. For a sample of 400 individuals who filed a tax return between April 10 and 15, the sample mean refund was $910. Based on prior experience a population standard deviation of o = $1,600 may be assumed. What is the p-value? c. At a = 0.05, what is your conclusion? d. Repeat the preceding hypothesis test using the critical value approach.

27. Price of Good Red Wine. According to the Vivino website, the mean price for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is $32.48. A New England-based lifestyle magazine wants to determine if red wines of the same quality are less expensive in Providence, and it has collected prices for 56 randomly selected red wines of similar quality from wine stores throughout Providence. The mean and standard deviation for this sample are $30.15 and $12, respectively. LO 1, 2,5 a. Develop appropriate hypotheses for a test to determine whether the sample data support the conclusion that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48. b. Using the sample from the 56 bottles, what is the p-value? c. Ata = 0.05, what is your conclusion? d. Repeat the preceding hypothesis test using the critical value approach. 31. Chocolate Consumption. The United States ranks ninth in the world in per capita chocolate consumption; Forbes reports that the average American eats 9.5 pounds of chocolate annually. Suppose you are curious whether chocolate consumption is higher in Hershey, Pennsylvania, the location of the Hershey Company’s corporate headquarters. A sample of 36 individuals from the Hershey area showed a sample mean annual consumption of 10.05 pounds and a standard deviation of s = 1.5 pounds. Using & = 0.05, do the sample results support the conclusion that mean annual consumption of chocolate is higher in Hershey than it is throughout the United States? LO 1,2, 5

37. Union Membership. The U.S. Bureau of Labor Statistics reports that 10.2% of U.S. workers belonged to unions in 2018. Suppose a sample of 400 U.S. workers is collected in 2023 to determine whether union efforts to organize have increased union membership. LO 1, 2, 6 a. Formulate the hypotheses that can be used to determine whether union membership increased in 2023. b. If the sample results show that 47 of the workers belonged to unions, what is the p-value for your hypothesis test? c. Ata = 0.05, what is your conclusion? 38. Attitudes toward Supermarket Brands. A study by Consumer Reports showed that 64% of supermarket shoppers believe supermarket brands to be as good as national name brands. To investigate whether this result applies to its own product, the manufacturer of a national name-brand ketchup asked a sample of shoppers whether they believed that supermarket ketchup was as good as the national brand ketchup.LO 1, 2, 6 a. Formulate the hypotheses that could be used to determine whether the percentage of supermarket shoppers who believe that the supermarket ketchup was as good as the national brand ketchup differed from 64%. b. If a sample of 100 shoppers showed 52 stating that the supermarket brand was as good as the national brand, what is the p-value? c. Ata = 0.05, what is your conclusion? d. Should the national brand ketchup manufacturer be pleased with this conclusion? Explain.

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