课程名称︰统计学一下 课程性质︰必修 课程教师︰雷立芬 开课学院：管理学院 开课系所︰国企系 考试日期（年月日）︰2012/04/11 考试时限（分钟）：180分 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 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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