課程名稱︰統計學一下
課程性質︰必修
課程教師︰王衍智
開課學院：管理學院
開課系所︰財務金融學系
考試日期（年月日）︰102.04.09
考試時限（分鐘）：90
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
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 ?
標準常態表: http://imgur.com/32fAQA5
卡方表: http://imgur.com/upkwL5n