课程名称︰初级统计学下 课程教师︰张宏浩 开课学院：管理学院 开课系所︰会计系 考试日期（年月日）︰2010年6月22日 考试时限（分钟）：13:20-16:10 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 1.(10%)Four-o'clock, Mirabilis jalapa, are plants native to tropical America. Individual four-o'clock plants can have red, white or pink flowers. According to Mendelian genetic principles, self-pollination of pink-flowered plants should produce progeny that have red, pink and white flowers in a 1:2:1 ratio. A scientist self-pollinates several pink-flowered plants and produces 240 progeny with 55 that are red-flowered, 132 that are pink-flowered and 53 that are white-flowered. Are these data reasonably consistent with the m=Mendelian model?(α=0.05) 2.(10%)Wang Corporation is interested in determining whether a relationship exists between the commuting time of its employees and the level of stress- related problems observed on the job. A study of 123 assembly-line workers reveal the following: Commuting time High Moderate Low Total Under 15 min 10 6 19 35 15-45min 15 9 29 53 Over 45 min 20 7 8 35 Total 45 22 56 123 At the 0.01 level of significance, is there evidence of a significant relationship between commuting time and stress level? (Note:you are required to specifically indicate your null and alternative hypotheses) 3.(15%)A marketing analyst for a shoe manufacturer is considering the development of a new brand of walking shoes. The marketing analyst wants to determine which variables to use in predicting durability. Two independent variables under consideration are X1(FOREIMP), a measurement of the forefoot shock-absorbing capability, and X2(MIDSOLE), a measurement of the change in impact properties over time. The dependent variable Y is LTIMP, a measurement of the shoe's durability after a repeated impact test. A random sample of 21 types of currently manufactured walking shoes was selected for testing, with the following incomplete results: Table 1 Variable Coefficients Standard Error t statistics Intercept -0.02686 0.06905 (a) FOREIMP 0.79116 0.02695 NA MIDSOLE 0.60484 0.07174 NA Table 2 Source Degree of Freedom Sum of Squares Regression 2 90 Error 18 130 Total 20 220 <PS>SSR(X1)=45, SSR(X2)=25, α=0.05 (1)(5%)Please caculate (a) in Table 1, and specify what is the definition of t statistics in table in. (with its null and alternative hypotheses) (2)(5%)Please use Table 2 to decide whether there is a significant relationship between LTIMP and FOREIMP (note: assume you do not have table 1, so you are forbidden to use information from table 1 to answer this question.) (3)(5%)Please compute the coefficients of partial determination of MIDSOLE, and interpret their meaning. 4.下表为A公司5种营养补给品与B公司6种营养补给品每100克之蛋白质含量(单位:克) A公司 B公司 5.03 4.5 5.36 3.7 5.24 5.0 5.23 4.0 5.69 4.9 5.7 检定A公司产品与B公司产品每百克之蛋白质含量之中位数是否有显着性差异(显着水准 为0.05)。 (1)(7%)使用Wilcoxon Rank Sum 检定法。 (α=0.05, n1=5, n2=6, (WL,WU)=(19,41)) (2)(8%)使用Mann-Whitney 检定法。 (n1=5, n2=6, P(U≦5)=0.041) 5.(10%)「安栗」、「如薪」两竞争的直销公司旗下销售员去年业绩如下:(单位:万元) 安栗 如薪 2.8 3.3 3.1 2.7 2.7 3.5 2.5 3.0 2.9 3.8 3.5 2.8 3.9 3.0 3.3 3.4 3.2 4.1 4.3 4.2 3.7 4.4 3.6 4.0 2.7 由於此属於大样本，在显着水准0.05下，Mann-Whitney检定法可近似常态分配，试以此 常态分配检定两直销公司销售元之业绩中位数是否有显着性差异? 6.(10%)抠思冻、哈跟答思、肚老爷三个品牌不同冰淇淋之热量如下:(单位:kcal) 抠思冻 哈跟答思 肚老爷 70 72 70 82 80 70 54 83 52 在显着水准0.05下，试以Kruskal-Wallis Rank Test 检定三种品牌所出冰淇淋热量中位 数是否有显着性差异。 7.(15%)Assume y, x1 and x2 represent the production yield, and capital uses of rice production in Taiwan. A regression model is set up as below: log(yi)=α+β1×log(x1i)+β2×log(x2i)+εi (a)Explain the economic meanings of the parameters β1 and β2? (b)How to conduct the test to see if the rice production technology is constant return to scale? Please write down the step carefully and the associated formula of the test. 8.(15%)Assume a researcher would like to examine the effects of education levels on wage. If the education levels are categorical and there are three categories defined in the sample(college, high school, less than high school) (a)How to set up a regression model to analyze this problem? (b)How to explain the meanings of parameters associated with the education levels? (c)How to test if the returns of college education is double than the returns of those didn't finish high school? Please write down the necessary hypotheses and test procedure associated with your model. 9.(10%)Given the sample of a series observation of (yi,xi), is there any possibility to examine whether the effects of xi on yi is a second-order non-linear relationship? How to set up the regression model and how to estimated coefficients. --

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