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| 2017/05/28 12:58:10瀏覽38｜回應0｜推薦0 | |
| 標題: 幫我解答這幾題統計學問題 發問: 1. For the past year I have spend about $4.00 a day for lunch, give or take a quarter ($0.25) or so. a. Draw a rough sketch of this distribution of daily expenditures (you may decide a reasonable variance by yourself). b. If, without looking at the bill, I paid for my lunch with a $5 bill and received... 顯示更多 1. For the past year I have spend about $4.00 a day for lunch, give or take a quarter ($0.25) or so. a. Draw a rough sketch of this distribution of daily expenditures (you may decide a reasonable variance by yourself). b. If, without looking at the bill, I paid for my lunch with a $5 bill and received $0.75 change, should I worry that I was overcharged? c. Explain the logic involved in your answer to part (b) d. What would be a Type II error? e. Similar to (b), but I have to pay $4.75 this time. Do you think I was overcharged? Assuming it is a normal distribution and the variance of the population is $0.25. Please explain the reason. In addition, please also explain why you adopt a two-tailed or one-tailed test. (It would be great if you can use computer to calculate the statistics, but you can simply do it by yourself and check the tables in the textbook.) 2. A recently admitted class of graduate students at a large state university has a mean GRE verbal score of 600 with a standard deviation of 50. The scores are reasonably normal distributed. a. One student, whose mother just happens to be a famous professor in that university, was admitted with a GRE score of 440. Should the local newspaper editor write a scathing editorial about favoritism? b. Please explain the null and alternative hypothesis you used above. 最佳解答: 1. a. 由題目知每日lunch費用之分佈範圍是 4 ± 0.25 取自然公差 ± 3σ, 即σ= 0.25/3 利用Excel繪製此費用之分佈草圖,步驟如下: 編輯 / 填滿 / 數列 在A2:A22製造數列 3.750,3.775,3.800,.....,4.250 B2輸入公式 =NORMDIST(A2,4,0.25/3,FALSE) 再用填滿控點往下拉到B22. 利用A2:B22作折線圖,結果如下: (下圖即Ans) 圖片參考：http://imgcld.yimg.com/8/n/AC09299269/o/20131120164032.jpg b. 5 - 0.75 = 4.25 4.25恰落在+ 3σ邊界 查標準常態表得P(Z>3) = 0.00135 , 其機率極低 Ans: 很有可能索價過高(被多收錢了) c. P( Z > 3 ) = 0.00135 < 0.01, 已達非常顯著水準. Ans: 費用大於或等於$4.25之機率僅0.00135,已達非常顯著水準, 故可判定索價過高. d. Ans: Type II error 簡要的意義即"壞的卻判定成好的", 此例是指,實際費用分佈之中心值已偏離原分佈之中心值 (標準差亦可能有所變動),但因為費用在 $ 3.75~4.25之間, 故以為費用之分佈沒有變動而誤判收費合理. e. (4.75-4) / 0.5 = 1.5 查表得 P( Z > 1.5 ) = 0.0668 > 0.05 Ans: (1) 收費合理(索價並無明顯過高). (2) 此屬單尾檢定. 2. a. (440-600) / 50 = -3.2 查表得 P( Z < -3.2 ) = 0.0007 < 0.01 , 已達非常顯著水準. Ans: 此學生非常明顯是靠關係入學,報社應發表社論抨擊此事. b. Ans: H0: mean GRE score = 600 H1: mean GRE score < 600
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