课程名称︰统计学一下 课程性质︰必修 课程教师︰王衍智 开课学院：管理学院 开课系所︰财务金融学系 考试日期（年月日）︰102.04.09 考试时限（分钟）：90 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : Statistic II Mock exam Time:18:30~20:00 Part I : Multiple choices questions (3 points for each) 1. A simple random sample of 100 college students was interviewed. They were asked what size pizza they usually order and what their favorite topping is. The results are presented below: Topping Size Shrimp Veggie Cheese Total Small 18 11 6 35 Medium 14 12 7 33 Large 3 9 20 32 Total 35 32 33 100 What would be the null hypothesis for a chi-square test based on these data? A) Pizza topping and pizza size are independent. B) The average pizza size is the same for shrimp, veggie, and cheese pizzas. C) The distribution of pizza topping is the same for small, medium, and large pizzas. D) The distribution of pizza size is different for the three different pizza toppings. 2. Following previous question, under the null hypothesis that there is no association between pizza size and pizza topping, what is the value of the expected count for a small shrimp pizza ? A) 11.67 B)12 C)12.25 D)13 3. Following previous question, what are the appropriate degrees of freedom for the chi-square statistic? A) 3 B) 4 C) 6 D) 8 4. Following previous question, what is the contribution to the chi-square statistics? A)-90 B)10 C)22.1 D)112.1 5. The distribution of Statistics class A is: Grade 0~20 20~40 40~60 60~80 80~100 Count 10 16 35 22 17 Please compute mean of the distribution (hint: use the mid-point to compute mean) A)54 B)60 C)63 D)66 6. Following previous question, what is the degree of freedom in this goodness of fit test by Chi-square test? A)2 B)3 C)4 D)5 7. Following previous question, what is the theoretical cumulative probability of grade below 20 under normal distribution(given standard deviation 23.95)? A)5.21% B)7.78% C)9.12% D)10.31% 8. Following previous question, what is the value of Chi-square test? A) Below 2 B) ranged 2~2.5 C) ranged 2.5~3 D) above 3 9. Following previous question, does this distribution obey a normal under Chi-square test? A) Yes B) No C) answer not available because of incomplete information 10.Which of the following one is the basic assumption that OLS estimation can be solved? A) Dependent variable obeys normal distribution. B) Independent variable is non-stochastic. C) Independent variable is not constant. D) Sum of residual is zero. Part II: Calculations 11. An investigation about vendor sales corresponding to market price in the product market. Eight months data are collected. (25 points) Sales 12 15 13 9 7 5 18 20 Price 3 4 5 6 7 3 10 12 Please answer question 11.a~11.e 11.a If we set regression model as SALES t = a0 + a1*PRICE t + Et , what are ^ ^ a0 and a1 by OLS? ^ 11.b What is the sample standard deviation of e by OLS ? 11.c What is the t-value where we test the null hypothesis, H0:a1=0 ? 11.d What is the R^2 ? 11.e What is predicted sales if price=20, what is the confidence interval at 5% significance level? Hint: t(α=5%)=2.45 12. We set regression model as: yi=a+bxi+ei,Σyi=100,Σxi=50,Σxi^2=1800, Σyi^2=2500,Σxiyi=1800, N=100. Please answer following question 12.a~12.c (15 points) ^ ^ 12.a Find a and b by OLS. ^ 12.b Find sample standard deviation of e by OLS. ^ 12.c Find Var(b) 13. Researcher studies the relation between number of computers a household has and the family income ($1000 per month). Regression model is specified as: Computer=a0+a1*income + u. She uses SAS and finds results in table below. Please answer questions 13.a~13.f by following regression results from SAS. The SAS System The REG Procedure Model: MODEL 1 Dependent Variable:Computer Root MSE 1.23848 R-square 0.3321 Dependent Mean 2.08000 Adj R-sq 0.3287 Coeff Var 59.54248 Number of Observations Read 200 Number of Observations Used 200 Analysis of Variance Source DF Sum of Squares Mean Square F value Pr>F Model 1 151.01939 151.01939 98.46 <.0001 Error 198 303.70061 1.53384 Corrected Total 199 454.72000 Parameter Estimates Variable DF Parameter Estimate Standard Error t Value Pr>│t│ Intercept 1 -0.04760 0.23161 -0.21 0.8374 Income 1 0.70880 0.07143 9.92 <.0001 13.a Is the regression model correctly specified under F-test? 13.b Let number of computers=Y. Family income=X. What is the theoretical incremental computer a household will have if it earns additional $10,000 per month? 13.c Using the conclusion of the regression result, what happens if a household earn zero income? 13.d What is the R^2 if we regress income on number of computers (income=b0+b1*computer + u) 13.e If we write slope estimator as a linear form:Ki*income i,what is the Σki? 13.f What is Σki^2 ? 标准常态表: http://imgur.com/32fAQA5 卡方表: http://imgur.com/upkwL5n --

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