Testing Hypotheses: One Sample Tests

As the bottom fell out of the oil market in early 1986, educators in Texas worried about how the resulting loss of state revenues (estimated to be about $100 million for each $1 decrease in the price of a barrel of oil) would affect their budgets. The state board of education felt the situation would not be critical as long as they could be reasonably certain that the price would stay above $18 per barrel. They surveyed 13 randomly chosen oil economists and asked them to predict how low the price would go before it bottomed out. The 13 predictions average $21.60, and the sample standard deviation was $4.65. At α = 0.01, is the average prediction significantly higher than $18.00? Should the board conclude that a budget crisis is unlikely? Exp lain.

The data-processing department at a large life insurance company has installed new color video display terminals to replace the monochrome units it previously used. The 95 opera- tors trained to use the new machines averaged 7.2 hours before achieving a satisfactory level of performance. Their sample variance was 16.2 squared hours. Long experience with operators on the old monochrome terminals showed that they averaged 8.1 hours on the machines before their performances were satisfactory. At the 0.01 significance level, should the supervisor of the department conclude that the new terminals are easier to learn to operate?

For a sample of 60 women taken from a population of over 5,000 enrolled in a weight- reducing program at a nationwide chain of health spas, the sample mean diastolic blood pressure is 101 and the sample standard deviation is 42. At a significance level of 0.02, on average, did the women enrolled in the program have diastolic blood pressure that exceeds the value of 75?

Realtor Elaine Snyderman took a random sample of 12 homes in a prestigious suburb of Chicago and found the average appraised market value to be $780,000, and the standard deviation was $49,000. Test the hypothesis that for all homes in the area, the mean appraised value is $825,000 against the alternative that it is less than $825,000. Use the 0.05 level of significance.

If a sample of 25 observations reveals a sample mean of 52 and a sample variance of 4.2, test the hypothesis that the population mean is 65 against the alternative hypothesis that it is some other value. Use the 0.01 significance level.

Given a sample mean of 94.3, a sample standard deviation of 8.4, and a sample size of 6, test the hypothesis that the value of the population mean is 100 against the alternative hypothesis that it is less than 100. Use the 0.05 significance level.

Picosoft, Ltd., a supplier of operating system software for personal computers, was planning the initial public offering of its stock in order to raise sufficient working capital to finance the development of a radically new, seventh-generation integrated system. With current earnings of $1.61 a share, Picosoft and its underwriters were contemplating an offering price of $21, or about 13 times earnings. In order to check the appropriateness of this price, they randomly chose seven publicly traded software firms and found that their average price/earnings ratio was 11.6, and the sample standard deviation was 1.3. At α = 0.02, can Picosoft conclude that the stocks of publicly traded software firms have an average P/E ratio that is significantly different from 13?

Given a sample mean of 83, a sample standard deviation of 12.5, and a samplesize of 22, test the hypothesis that the value of the population mean is 70 against the alternative that it is more than 70. Use the 0.025 significance level.

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?

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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Testing Hypotheses: One Sample Tests

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