課程名稱： 統計學 課程性質： 整開 課程範圍： Chapter 1 - Chapter 10.9，重點在 Chapters 7, 8, 9, 10 開課教師： 丁兆平 開課學院： 商學院 開課系級： 統計系 考試日期(年月日)： 2014/1/14 考試時限(Mins)： 120 min 附註： 有關解 hypothesis testing 問題的注意事項：最後寫結論時務必完整，請參考下例。 Reject H0 (or do not reject H0) at level 0.01 (or else) 再加上文字敘述，如 "The data iindicates or suggests that ......" 不可只寫 Reject H0 or do not reject H0. 試題本文： 1. The price of shares of bank of Florida at the end of trading each day for last year followed the normal distribution. Assume there were 240 trading days in the year. The mean price was $42 per share and the standard deviation was $2.25 per share. a. What percent of the days was the price over $45? How many days would you estimate? (10 pts) b. What was the stock's price on the highest 15 percent of days? (5 pts) 2. A recent study indicated that women took an average of 8.6 weeks of unpaid leave from their jobs after the birth of a child. The shape of this distribution is not known, but the maximum number of unpaid leave is 16 weeks and the minimun is 4 weeks. We select a sample of 36 women who recently returned to work after the birth of a child. What is the approximate probability that the mean of this sample is at least 8.8 weeks. (10 pts) 3. In a recent Zogby poll of 1,000 adults in the United States, 613 said they believe other forms of life exist elsewhere in the universe. a. Construct the 99% confidence interval for the population propotion of those believing life exists elsewhere in the universe. Does your result imply that a majority of Americans believe life exists outside of earth? (10 pts) b. At the 0.01 significance level can we conclude that half of the Americans believe life exist outside of earth. (10 pts) 4. The auditor of Taiwan's Bug Lotto needs an estimate of proportion of residents who regularly play the lottery. From previous experience, about 40 regularly play, but the auditor would like some current information. How large a simple is necessary for the estimate to be within 3 percentage points, with a 98 percent level of confidence? (5 pts) 5. Suppose that when a transistor of a certain type is subjected to an accelerated life test, the life time (in weeks) has an exponential distribution with mean 24 weeks. a. What is the probability that a transistor will last between 12 and 24 weeks? (10 pts) b. Suppose that the test will actually be terminated after t weeks. What value of t is such that only 1% of all transistors would still operating at termination? (10 pts) 6. An insurance company, based on past experience, estimates the mean damage for a national disaster in its area is NT$200,000. After introducing several plans to prevent loss, they randomly sample 200 policyholders and find the mean amount per claim was NT$192,000 with a standard deviation of NT$52,000. a. Does it appear the pervention plans were effective in reducing the mean amount of a claim? Use the 0.05 significance level (10 pts) b. What is the p-value? (5 pts) 7. In tast year the mean fare to fly from Charlotte, North Carolina, to Seattle,Washington, on a discount ticket was $267. A random sample of 13 round-trip discount fares on this route last month gives: 321 286 290 330 310 250 270 280 299 265 291 275 281 a. At the 0.01 significance level can we conclude that the mean fare has increased? (10 pts) b. Any assumption needed in order to answer (a)? (5 pts) PO文看考試注意事項才發現附註上的內容，囧 --

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