世新大學九十一學年度碩士班招生考試試題

系所別	考試科目
平面傳播科技學系碩士班	統計學

※ 考生請於答案卷內作答

1. 專有名詞20％

a. Hypothesis testing （需含有null hypothesis , TypeⅠerror , TypeⅡerror , significance level）

b. Statistics independent（請用conditional probability 解釋）

c. Maximum Likelihood Estimate

d. Mean , median , percentile , standard deviation ,

e. Sample mean , sample variance

2. 證明下列敘述10％

If two random variables are independent, they are uncorrelated. The converse is not true in general.

3. 20%

量測1000人的體重身高。設體重平均150有標準差異20，身高平均66有標準差異3，身高與體重的correlation coefficient 為0.6。用迴歸估計下例各式：

a. 身高66的人之體重

b. 身高72的人之體重

c. 體重160的人之身高

d. 體重為低於所有被測人體重平均值的2倍標準差的人之身高

4. 10％

In one pocket, I have two quarters; in the other, I have a quarter and a nickel. My toddler reaches into one of my pockets and grabs a coin. Assume that she picks the pocket and the coin randomly, and that the chance she reaches into each pocket is 50%, and the chance that she pulls out each of the two coins in each pocket is the same. What is the conditional probability that the second coin in the pocket she reaches into is a quarter, given that the coin she pulls out is a quarter?

5. 10％（本題為單選若答錯倒扣一分）

The next five questions refer to the list {0,1,0,-3,-1}

a. The mean is: (a) 1/6, (b) 0, (c) 1, (d) 0, (e) none of the above

b. The median is: (a) –1, (b)0, (c) 1, (d) 2, (e) none of the above

c. The root mean square is: (a) sqrt(5), (b) sqrt(3 1/3), (c) sqrt(20), (d) 2, (e) none of the above

d. The stander deviation is: (a) sqrt(22/6), (b) sqrt(5), (c) aqrt(3 1/3) (d) sqrt(20) (e) none of the above

e. The 25^th percentile is: (a) –3, (b) –1, (c)0, (d) 1, (e) none of the above

6. (20%) 現欲檢定 H₀: μ≧3 。設可容忍的型Ⅰ錯誤的機率為α＝0.01，

H₁: μ＜3

型Ⅱ的錯誤機率在μ＝2.95時為0.05（即β＝0.05），又假設已知母體標準差為0.25。試問至少應抽取多少樣本，才能達到假設的α, β水準？（查表得知標準常態分配Z_0.01＝2.33，Z_0.05＝1.64）

7. （10％）設隨機變數X為常態分配N（μ, σ²），試求μ, σ² 之最大概似估計式Maximun Likelyhood Estimate。