课程名称︰统计学 上 课程性质︰ 课程教师︰雷立芬 开课学院：管院 开课系所︰国企系 考试日期（年月日）︰ 10/01/13 考试时限（分钟）：3 hr 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 1. a. Determine the sample size necessary to estimate a population mean to within 1 with 90% confidence given that the population standard deviation is 10 (5%) b. Suppose that the sample mean was calculated as 150. Estimate the population mean with 90% confidence.(5%) 2. Previous experience shows the mean and variance of a given process to be 45 and 36, respectively. Researchers are testing to determine whether these values have changed. They gather the following dozen measurements of the process. Assume the measurements are normally distributed. a. Use these data and α=0.01 to test the hypothesis that population mean is greater than 45.(16%) b. Estimate with 95% confidence population mean. Explain the result.(7%) c. Use these data and α=0.05 to test the hypothesis tha population variance has changed.(10%) d. Estimate with 99% confidence the population variance. Explain the result. (7%) 52 44 51 58 48 49 38 49 50 42 55 51 3. Suppose a population is normally distributed as N(μ,36). We will conduct a hypothesis test with: H0:μ≧20 versus H1:μ<20, where α=0.05, n=49. a. Explain Type II error (4%) b. What would bt the power of the test if the actual mean weere 19?(16%) 4. Suppose you are testinf H0: p=0.29 versus H1:p≠0.29. A random sample of 740 items show that 207 have this characteristic. With a 0.05 probability of committing a type I error, test the hypothuesis. a.Explain type I error(4%) b.For the p-value method, what is the probability of the calculated Z value for this problem? CAn you reject the null hypothesis? why?(8%) c.If you had used the critical value method, what would the two critical values be? Can you reject the null hypothesis? Why? (9%) d.Estimate with 95% confidence the population propotion. Can you reject the null hypothesis? Why (9%) --

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