課程名稱︰統計學一下
課程性質︰必修
課程教師︰雷立芬
開課學院：管理學院
開課系所︰國企系
考試日期（年月日）︰2012/04/11
考試時限（分鐘）：180分
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. A two-factor analysis of variance experiment was performed with r=3 (levels
of factor A). c=4 (levels of factor B), and k=20. The following sums of squares
were computed:
SS(A)=1560, SS(B)=2880, SS(AB)=7650, SS(Total)=42450
(a) Present the ANOVA table.
(b) Test at the 1% significance level to determine whether differences exist
between the levels of factor A, the levels of factor B, and interaction between
factor A and B.
2. A nationwide market research study is undertaken to determine the preference
of various age groups of males for different team sports. A random sample of
1000 men is selectd, and each individual is asked to indicate his favorite team
sport. The result are follows:
Sport
Age Group Baseball Football Basketball Hockey Total
Under 20 26 47 41 36 150
20-29 38 84 80 48 250
30-39 72 68 38 22 200
40-49 96 48 30 26 200
50 and over 134 44 18 4 200
Total 366 291 207 136 1000
At the 0.05 level of significance, is there evidence of a significant relation-
ship between men's ages and their preferences in sports?
3. Use the Kruskal-Wallies test on the following data to determine if the popu-
lations are identical. Use α=0.05.
Sample 1 27 33 18 29 41 52 75
Sample 2 37 12 17 22 30
Sample 3 19 12 33 41 28 18
4. The following data was collected on nonconformances for a period of 10 days.
Day Sample Size Nonconformances
1 111 12
2 93 14
3 105 10
4 92 18
5 117 22
6 88 14
7 117 15
8 87 13
9 119 14
10 107 16
(a) Which control chart do you want to use?
(b) What are the LCL and UCL?
(c) Are there any special causes of variation?
5. The manufactur of a nationally distributed brand of potato chips would like
to determine the feasibility of changing the product package from a cellophane
bag to an unbreakable container. The product manager believes that there would
be three possible market responses to a change in product packaging: weak, mo-
derate, and strong. The projected payoffs , in increased or decreased profit
as compared with the current packaging, are as follows:
STRATEGY
Event Use New Package Keep Old Package
Weak national response -$4,000,000 0
Moderate national response 3,000,000 0
Strong national response 5,000,000 0
On the basis of past experience, the product manager assigns the following pro-
babilities to the different levels of national response: P(weak)=0.30; P(mode-
rate)=0.60; P(strong)=0.10.
(a) Set up the opportunity loss table.
(b) Compute the expected value of perfect information and explain it.
(c) Should the company offer this new product package? Why?
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