Chapter 8 and 9 Practice problems

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8.50. Use the following information to compute the confidence interval for the population proportion. a. n = 715 and x = 329, with 95% confidence b. n = 284 and with 90% confidence c. n = 1250 and , with 95% confidence d. n = 457 and x = 270, with 98% confidence 8.52. Determine the sample size necessary under the following conditions. a. To estimate μ with σ = 44, E = 3, and 95% confidence b. To estimate μ with a range of values from 20 to 88 with E = 2 and 90% confidence c. To estimate p with p unknown, E = .04, and 98% confidence d. To estimate p with E = .03, 95% confidence, and p thought to be approximately .70 8.59. Is the environment a major issue with Americans? To answer that question, an analyst conducts a survey of 1255 randomly selected Americans. Suppose 714 of the sampled people replied that the environment is a major issue with them. Construct a 95% confidence interval to estimate the proportion of Americans who feel that the environment is a major issue with them. What is the point estimate of this proportion? 8.69. A research firm has been asked to determine the proportion of all restaurants in the state of Ohio that serve alcoholic beverages. The firm wants to be 98% confident of its results but has no idea of what the actual proportion is. The firm would like to report an error of no more than .05. How large a sample should it take? 9.44. Use the information given and the eight-step approach to test the hypotheses. Let α = .01. H0: μ = 36 Ha: μ ≠ 36 n = 63 σ = 5.93 9.45. Use the information given and the eight-step approach to test the hypotheses. Let α = .05. Assume that the population is normally distributed. H0: μ = 7.82 Ha: μ < 7.82 n = 17 = 7.01 s = 1.69

9.48. Solve for the value of beta in each of the following problems. a. H0: μ = 130 Ha: μ > 130 n = 75 σ = 12 α = .01 The alternative mean is actually 135. b. H0: p = .44 Ha: p < .44 n = 1095 α = .05 The alternative proportion is actually .42. 9.53. A computer manufacturer estimates that its line of minicomputers has, on average, 8.4 days of downtime per year. To test this claim, an analyst contacts seven companies that own one of these computers and is allowed to access company computer records. It is determined that, for the sample, the average number of downtime days is 5.6, with a sample standard deviation of 1.3 days. Assuming that number of downtime days is normally distributed, test to determine whether these minicomputers actually average 8.4 days of downtime in the entire population. Let α = .01. 9.58. According to Gartner Inc., the second-largest share of the worldwide PC market is held by Hewlett- Packard with 19.8%. Suppose that a market researcher believes that Hewlett-Packard holds a higher share of the market in the western region of the United States. To verify this theory, he randomly selects 428 people who purchased a personal computer in the last month in the western region of the United States. Of these purchases, 90 were Hewlett-Packard computers. Using a 1% level of significance, test the market researcher’s theory. If the market share is really .22 in the western region of the United States, what is the probability of making a Type II error?

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