世新大學八十九年學年度碩士班招生考試試題
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系所別 |
考試科目 |
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經濟學係碩士班 |
統計學 |
Please answer each of the following problems in sequence. The scores are given for each problem. You may use your own pocket calculator for needed computations.
1. Consider a sample of size 2 drawn without replacement from an urn containing three balls, numbered 1 2, and 3. Let X be the smaller of the two numbers drawn and Y the larger. (各小題4分)
(a) Find the joint discrete density function of X and Y.
(b) Find the conditional distribution of Y given X=1.
(c) Find COV[X,Y].
2.
̅ ̅
Let Z1, Z 2, be a
random sample of size 2 from N (0,1) and X1, X2 a random
sample of size 2 from N(1,1). Suppose the Zi’s are independent of
the Xj’s. Please answer the following questions:(各小題4分)
(a) What is the distribution of X +Y?
(b) What is the distribution of (Z1+Z2) / {[(X2-X1)2 + (Z2+Z1)2] / 2}0.5 ?
(c) What is the distribution of [(X1 - X2) 2 + (Z1-Z2) 2 + (Z1+Z2) 2] / 2?
(d) What is the distribution of (X2+X1-2) 2 / (X2 – Z1) 2?
3. 下列資料是五名公司行號推薦來的經理級主管，參加企管研習班所得各科的成績，試以變異數分析法，回答下列各小題。(各小題4分)
(a) 以α =
0.01檢定各課程的難易程度相同。
(b) 以α = 0.01檢定各學員的學習能力相同。
(c) 求共同變異數σ2之99%的信賴區間。
F(3, 12, 0.01) = 5.95, F(4, 12, 0.01) = 5.41, X2(12,
0.995) = 3.07, X2(12, 0.005) = 28.30
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企業管理 |
企業診斷 |
財務分析 |
高階管理 |
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學員一 |
68 |
57 |
33 |
61 |
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學員二 |
83 |
94 |
91 |
86 |
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學員三 |
72 |
81 |
63 |
59 |
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學員四 |
55 |
73 |
77 |
66 |
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學員五 |
92 |
68 |
75 |
87 |
4. Three admission test preparation programs are being evaluated. The scores obtained by a sample of 20 people who used the test preparation programs provided the data shown below. Use the Kruskal-Wallis test to determine whether there is a significant difference among the three test preparation programs. Use α =0.01.(各小題4分)
(a) Write down the null and alternative hypotheses, also the decision rule.
(b) Conduct the test and arrive your conclusion. (X2(2, 0.01) = 9.21)
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Program A |
540 |
400 |
490 |
530 |
490 |
610 |
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Program B |
450 |
540 |
400 |
410 |
480 |
370 |
550 |
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Program C |
600 |
630 |
580 |
490 |
590 |
620 |
570 |
5. A cola-dispensing machine is set to dispense 9.00 ounces of cola per cup, with a standard deviation of 1.00 ounces. The manufacturer of the machine would like to set it in such a way that for samples of 36, 5 percent of the sample means will be greater than the upper control limit, and 5 percent of the sample means will be less than the lower control limit. (各小題4分)
(a) At what value should the control limit be set?
(b) What is the probability that if the population mean shifts to 8.9, this change will not be detected?
(c) What is the probability that if the population mean shifts to 9.3, this change will not be detected?
6. 若犯罪率可能受到所得水準、男女結構比、失業率、教育程度的影響，則無人以犯罪率為因變數，而所得水準、男女結構比、失業率、教育程度為自變數，進行回歸配適。試問：
6.1.請個別檢定在10%的顯著水準下(臨界值為2.00)，所得水準、男女結構比、失業率、教育程度分別對犯罪率是否有影響？(5分)
6.2.請聯合檢定在10%的顯著水準下(臨界值為2.00)，所得水準、男女結構比、失業率、教育程度至少有一變數對犯罪率是否有影響？(5分)
6.3.請分別計算在MODEL-B、MODEL-C、MODEL-D、 MODEL-E中的 R2？
6.4. 在MODEL-B、MODEL-C、MODEL-D、 MODEL-E中，以模型選擇的標準來看，何者為最佳？ (請說明以何為標準) (5分)
6.5.以MODEL-B而言，若所得水準再估計時原使用百萬元為單位，今若改採用元為單位，試問會對迴歸係數的估計有何影響，為什麼？(10分)
