Before the 1973 oil embargo and subsequent increases in the price of crude oil, gasoline usage in the United States had grown at a seasonally adjusted rate of 0.57 percent per month, with a standard deviation of 0.10 percent per month. In 15 randomly chosen months between 1975 and 1985, gasoline usage grew at an average rate of only 0.33 percent per month. At a 0.01 level of signifi cance, can you conclude that the growth in the use of gasoline had decreased as a result of the embargo and its consequences?
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The Bay City Bigleaguers, a semiprofessional baseball team, have the player who led the league in batting average for many years. For thé past several years, Joe Carver’s batting average has had a mean of .343, and a standard deviation of .018. This year, however, Joe’s average was only .306. Joe is renegotiating his contract for next year, and the salary he will be able to obtain is highly dependent on his ability to convince the team’s owner that his batting average this year was not significantly worse than in previous years. If the owner is willing to use a 0.02 significance level, will Joe’s salary be cut next year?
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A ketchup manufacturer is in the process of deciding whether to produce a new extra-spicy brand. The company’s marketing-research department used a national telephone survey of 6,000 households and found that the extra-spicy ketchup would be purchased by 335 of them. A much more extensive study made 2 years ago showed that 5 percent of the households would purchase the brand then. At a 2 percent significance level, should the company conclude that there is an increased interest in the extra-spicy flavor?
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Steve Cutter sells Big Blade lawn mowers in his hardware store, and he is interested in comparing the reliability of the mowers he sells with the reliability of Big Blade mowers sold nationwide. Steve knows that only 15 percent of all Big Blade mowers sold nationwide require repairs during the first year of ownership. A sample of 120 of Steve’s customers revealed that exactly 22 of them required mower repairs in the first year of ownership. At the 0.02 level of significance, is there evidence that Steve’s Big Blade mowers differ in reliability from those sold nationwide?
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Grant, Inc., a manufacturer of women’s dress blouses, knows that its brand is carried in 19 per- cent of the women’s clothing stores east of the Mississippi River. Grant recently sampled 85 women’s clothing stores on the West Coast and found that 14.12 percent of the stores carried the brand. At the 0.04 level of significance, is there evidence that Grant has poorer distribution on the West Coast than it does east of the Mississippi?
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From a total of 10,200 loans made by a state employees’ credit union in the most recent 5-year period, 350 were sampled to determine what proportion was made to women. This sample showed that 39 percent of the loans were made to women employees. A complete census of loans 5 years ago showed that 41 percent of the borrowers then were women. At a significance level of 0.02, can you conclude that the proportion of loans made to women has changed sig- nifi cantly in the past 5 years?
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Feronetics specializes in the use of gene-splicing techniques to produce new pharmaceutical compounds. It has recently developed a nasal spray containing interferon, which it believes will limit the transmission of the common cold within families. In the general population, 15.1 percent of all individuals will catch a rhinovirus-caused cold once another family member contracts such a cold. The interferon spray was tested on 180 people, one of whose family members subsequently contracted a rhinovirus-caused cold. Only 17 of the test subjects devel- oped similar colds. (a) At a significance level of 0.05, should Feronetics conclude that the new spray effectively reduces transmission of colds? (b) What should it conclude at α = 0.02? (c) On the basis of these results, do you think Feronetics should be allowed to market the new spray? Explain.
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Some financial theoreticians believe that the stock market’s daily prices constitute a “random walk with positive drift.” If this is accurate, then the Dow Jones Industrial Average should show a gain on more than 50 percent of all trading days. If the average increased on 101 of 175 randomly chosen days, what do you think about the suggested theory? Use a 0.01 level of significance.
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MacroSwift estimated last year that 35 percent of potential software buyers were planning to wait to purchase the new operating system, Window Panes, until an upgrade had been released. After an advertising campaign to reassure the public, MacroSwift surveyed 3,000 people and found 950 who were still skeptical. At the 5 percent significance level, can the company conclude the proportion of skeptical people has decreased?
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Rick Douglas, the new manager of Food Barn, is interested in the percentage of customers who are totally satisfied with the store. The previous manager had 86 percent of the customers totally satisfied, and Rick claims the same is true today. Rick sampled 187 customers and found 157 were totally satisfied. At the 1 percent significance level, is there evidence that Rick’s claim is valid?
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