課程名稱︰統計學一上 課程性質︰系定必修 課程教師︰雷立芬 開課學院：管理學院 開課系所︰國際企業學系 考試日期（年月日）︰98年1月14日 考試時限（分鐘）：三小時 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1. The number of cars sold annually by used car salesperson is normally distributed with a standard deviation of 15. A random sample of 15 salesperson was taken and the number of cars each sold is listed as follows. Find and interpret the 95% confidance interval estimate of the population mean. (10%) Test to determine whether there is envidence that the population mean number of cars sold is greater than 66, using the p-value approach. (10%) At the 10% significance level, test the population variance is different from 225. (15%) 79 43 58 66 101 63 79 33 58 71 60 101 74 55 88 2. A school-board administrator believes that the average number of days absent per year among students is less than 10 days. From past experiences, he knows that the population standard deviation is 3 days. In testing to determine whether his believe is true, he could use one of the following plans: i. n=100 α=0.01 ii. n=75 α=0.05 iii.n=50 α=0.1 Define Type I and Type II error, respectively. (5%) Which plan has the lowest probability of Typr II error, given that the true population average is 9 days? (15%) 3. Part of a university professor's job is to publish his/her research. This task often entails reading a variety of journal articles to keep up to date. To help determine faculty standards, a dean of a business school surveyed a random sample of 12 professors across the country and asked them to count the number of journal articles they read in a typical month. These data are listed as follows. Estimate with 90% confidence the mean number of journal articles read monthly by prfessors. (12%) Interpret the mean of 90% confidence interval. (3%) At the 10% significance level, test to determine whether there is evidence that the population mean number of journal articles read by professors is greater than 23. (10%) 6 4 1 23 56 30 41 45 21 10 44 20 4. What type of educational background do CEOs have? In one survey, 433 CEOs of medium and large companies were asked whether they had an MBA degree. There were 114 MBAs. Determine the sample size necessary to estimate a population proportion of CEOs of medium and large companies who have MBAs to within 3% with 95% of confidence interval. (5%) Find and interpret the 93% confidence interval estimate of the population proportion. (5%) At the 1% significance level, determine whether there is evidence that the population proportion is less than 0.3. (10%) ***所有的假設檢定問題，須有完整而正確之假設與檢定過程。 --

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