Testing Hypotheses: Two Sample Tests

In October 1992, a survey of 120 macroeconomists found 87 who believed that the recession had already ended. A survey of 150 purchasing agents found 89 who believed the recession had ended. At α = 0.10, should you conclude that the purchasing agents were more pessimistic about the economy than the macroeconomists were?

Full length feature films earn huge profits for entertainment giant The Walt Disney Company. Hit movies, such as Aladdin, may earn more than $3000 million above their production costs.

The MBA program at Piedmont Business School offers Analytic Skills Workshop (ASW) during the summer to help entering students brush up on their accounting, economics, and mathematics. Program Director Andy Bunch wonders whether ASW has been advantageous to the students enrolled. He has taken random samples of grade-point averages for students enrolled in ASW over the past 5 years and for students who started the MBA program without ASW during the same time span. At α = 0.02, have the ASW students gotten signifi cantly higher GPAs? Should Andy advertise that ASW helps student achievement in the MBA program? xsn ASW 3.37 1.13 26 Non-ASW 3.15 1.89 35

Fifty-eight of 2,000 randomly sampled corporations had their 1995 federal income tax returns audited. In another sample of 2,500 corporations, 61 had their 1994 returns audited. Was the fraction of corporate returns audited in 1995 signifi cantly different from the 1994 fraction? Test the appropriate hypotheses at α = 0.01.

Ellen Singer asserted to one of her colleagues at Triangle Realty that homes in southern Durham County sold for about $15,000 less than similar homes in Chapel Hill. To test this assertion, her colleague randomly chose 10 recent sales in Chapel Hill and matched them with 10 recent sales in southern Durham County in terms of style, size, age, number of rooms, and size of lot. At α = 0.05, do the following data (selling prices in thousands of $) support Ellen’s claim? Chapel Hill 97.3 108.4 135.7 142.3 151.8 158.5 177.4 183.9 195.2 207.6 Durham County 81.5 92.0 115.8 137.8 150.9 149.2 168.2 173.9 175.9 194.4

The Dow-Jones Transportation Average is based on the closing prices of the common stocks of 20 airline, rail, and freight companies.

TV network executive Terri Black has just received a proposal and a pilot tape for a new show. Empty Nest No Longer is a situation comedy about a middle-aged couple whose two collegegraduate offspring cannot fi nd jobs and have returned home. Terri wonders whether the show will appeal to twenty-somethings as well as to an older audience. Figuring that people in her offi ce are reasonably representative of their age group in the population as a whole, she asks them to evaluate the pilot tape on a scale from 0 to 100, and gets the following responses. Age Responses 20–29 86 74 73 65 82 78 79 ≥ 30 63 72 68 75 73 80 (a) At a 0.05 signifi cance level, should Terri conclude the show will be equally attractive to the two age groups? (b) Independent of your answer to (a), do you think Terry should use the results of her offi ce survey to decide how to design an advertising campaign for Empty Nest No Longer? Explain.

A manufacturer of pet foods was wondering whether cat owners and dog owners reacted differently to premium pet foods. They commissioned a consumer survey that yielded the following data.Pet Owners Surveyed Number Using Premium Food Cat 280 152 Dog 190 81 Is it reasonable to conclude, at α = 0.02, that cat owners are more likely than dog owners to feed their pets premium food?

Robin Wendell has been offered a transfer from Pittsburgh to Boston, but is holding out for more money, “because the cost of living there is so much more.” Looking at a grocery receipt and deleting big-ticket items, Robin came up with 36 items under $2 with a mean of $0.98, standard deviation $0.43 in Pittsburgh. The recruiting manager stops by a Boston grocery store, and with the same $2.00 limit, buys 42 items, with a mean price of $1.07, standard deviation $0.38. Is Robin right that the cost of groceries is more in Boston than in Pittsburgh, at a confi dence level α = 0.01? What could be done to improve the analysis of cost of living in the two cities?

A group of British Physicians replicated a U.S. management survey of medical directors, asking which skills they considered useful and essential for their jobs.

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