課程名稱︰統計學上 課程性質︰ 課程教師︰游孝元 開課學院：管理學院 開課系所︰國企系 考試日期（年月日）︰2014/01/09 考試時限（分鐘）：14:30-16:30 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 一、(20%) Suppose the National Bureau of Economic Research(NBER) is conducting the global economic outlook for 2014. NBER randomly samples 965 persons and finds that 531 persons are optimistic about the US economy for this year. 1. Build the 95% confidence interval to estimate the proportion of people who are optimistic about the US economy in 2014. 2. Based on aforementioned estimate results, could NBER infer that a majority of people is optimistic about the US economy? 3. If you are not satisfied with the estimate results and think the interval you got is too wide, how could you improve and obtain the more precise estimates? 二、(20%)Fisherman in South California claim the average size of local lobsters is greater than 82 meters. Suppose you want to determine whether the true mean size of lobsters is higher than what the fishermen said, following samples come from your research team. (Significance level=0.05) ---------------------------- 70 , 86 , 88 , 93 , 104 , 99 ---------------------------- 1. Specify the statistic hypotheses 2. Process your test 3. Make conclusions based on your test results 三、(15%) Engineers want to know the variation in product length and further to understand if they are consistent with company production standards. 91 samples obtained from Type-015 machine show that the sample average and sample standard deviation are 1005.8 and 375.2 centimeters respectively 1. Use the sample data to find a 95% confidence interval for the engineer's interest. 2. State the required conditions making the confidence interval valid. 四、(15%)某茶飲公司品管部門希望了解其生產之罐裝茶飲重量是否符合規定(每罐300毫升 )，檢測人員隨機抽取50罐飲料進行檢測，結果得出樣本均數298毫升，樣本變異數 55毫升^2。假設顯著水準0.10，試問： 　1. 請替品管人員設立適當的虛無假說及對立假說 2. 計算檢定p-value，並據此寫出結論 五、(30%)假設母體機率分配如下: ----------------------------------- x │ 0 │ 2 │ 6 │ ----------------------------------- f(x)│ 0.25 │ 0.5 │ 0.25 │ ----------------------------------- 現自該母體採取抽出放回之方式隨機抽取2個樣本(x1、x2)，試問: 1. 試求母體均數及變異數 _ x1 + x2 _ 2. 令 x=------------ ，寫出 x 之抽樣分配 2 _ 3. 試求 x 之期望值與變異數，比較其與母體均數及變異數之關係 -------------------------------------------------------- 附表1 z分配 附表2 t分配臨界值表 附表3 卡方分配臨界值表 附表4 F分配臨界值表 --

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