義守大學 96 學年度博士班入學招生考試試題 系所 工業工程與管理學系
科目 統計學
【可使用計算機】※ 此為試題卷，考生請於答案卷上作答。 頁數1/2
第1 頁
1. If X and Y are independent Poisson random variables with respective means λ1 and λ2, then A. Calculate the distribution of X + Y. (10%)
B. Calculate the conditional expected value of X given that X + Y = n. (10%)
2. The board of regents at a university would like to determine if two variables are independent: employee classification (staff, faculty, administrator) and whether a single union should be the sole collective bargaining agent for employee benefits. A random sample of 200 employees is taken from employee records and each employee is classified according to both variables. The data are listed below.
Opinion on Collective Bargaining by Teacher's Union Employee
Classification Favor
Do Not
Favor Undecided Total
Staff 30 15 15 60 Faculty 40 50 10 100 Administrator 10 25 5 40
Total 80 90 30 200 Please write down the complete statistical hypothesis testing steps and make conclusion given that α=0.05 and χ02.95,4 =9.45, χ02.05,4 =0.71, χ02.95,9 =16.92 and χ02.05,9 =3.325. (20%)
3. An experiment is conducted to investigate factors influencing time needed to ride a bike to the top of a mountain. Factors investigated include A: Seat height; B: Generator; C: Handler; D: Transmission; E:
Rain Coat; F: Breakfast; G: Tires. All these factors are designed to use two levels. The ANOVA table is shown below.
A. Fill the blank of item A in the following ANOVA table given that F0.95,1,5=6.6, F0.99,1,5=16.26 and F0.999,1,5=47.18. (4%)
Analysis of Variance for y
Source DF SS MS F P
A
B 1 364.50 364.50 **
C 1 0.50 0.50 **
D 1 1300.50 1300.50 **
E 1 0.50 0.50 **
F 1 4.50 4.50 **
G 1 4.50 4.50 **
Error 0 * *
Total 7 1687.50 B. Which factors are critical? why? (3%)
C. In order to get the p value, how would you do? (3%)
D. Complete the ANOVA table to get p value of each critical factor and R2 of the model!
(10%)
義守大學 96 學年度博士班入學招生考試試題 系所 工業工程與管理學系
科目 統計學
【可使用計算機】※ 此為試題卷，考生請於答案卷上作答。 頁數2/2
第2 頁
4. A study investigates how alcohol concentration in blood (x1), weight (x2) and cans of beer drunk influencing opportunity of coming up an accident (y).
A.
Complete the following blanks. (15%)The regression equation is y = (1) – (2) x1 + (3) x2 + (4) x3 Predictor Coef SE Coef T P VIF Constant 72.344 2.455 (5) 0.000 x1 -542.21 82.99 (6) 0.000 17.1 x2 0.0305 0.1311 (7) 0.819 3.8 x3 7.538 1.018 (8) 0.000 13.9
S = (9) R-Sq = (10) R-Sq(adj) = 69.3%
Analysis of Variance
Source DF SS MS F P
Regression (11) 1780.86 (14) (16) 0.000 Residual Error (12) (13) (15)
Total 23 2430.00
B. What is the problem of this model and how would you amend it? (5%)
5. Ten brand A tires and ten brand B tires were tested and the distance to wear out in thousands of miles were recorded as follows.
1 2 3 4 5 6 7 8 9 10 Average Std dev
A 21 20 25 24 24 28 16 24 26 22 23 3.40
B 20 26 21 16 18 12 24 22 18 14 19.1 4.38
A. To test their difference, what kind of statistics testing tools could be used? (3%) B. To use the tool you mention, what assumption should be met? (3%)
C. Calculate the test statistic and make conclusion given that t18,0.95=1.73,t18,0.98=2.21, t18,0.99=2.55. (4%)
6. How many ways are there to test means of two samples under different situations? (10%)
