98年國立中山大學資訊管理學系統計學

1.

(A)

(B)

(C)

The degrees of freedom are 4.

(D)

(E)

None of the above.

2.

If a categorical independent variable contains 3 categories, then how
many dummy variable(s) will be needed to uniquely represent these
categories?

(A)

1

(B)

2

(C)

3

(D)

4

(E)

5

3.

An interaction term in a multiple regression model may be used when

(A)

the coefficient of determination is small

(B)

there is a curvilinear relationship between the dependent and
independent variables.

(C)

neither one of 2 independent variables contribute significantly to
the regression model.

(D)

(E)

one of 2 independent variables is categorical.

4.

(A)

(0.2534, 1.7847)

(B)

(0.2480, 2.575)

(C)

(0.2067, 2.1458)

(D)

(0.3041, 2.1417)

(E)

(0.8333, 8.3333)

5.

(A)

29.84

(B)

61

(C)

5.1993

(D)

4.476

(E)

5.0353

6.

(A)

(−2.0009, 24.0009)

(B)

(5.8802, 16.1198)

(C)

(8.6209, 13.3805)

(D)

(−16.1198, −5.8802)

(E)

(5.9647, 16.0353)

On average, one telephone call comes in every 30 seconds. It is known that
the number of telephone calls follows the Poisson distribution.

7.

The probability that no more than 2 telephone calls in 4 minutes is

(A)

0.67668

(B)

0.23810

(C)

0.01375

(D)

0.98625

(E)

0.76190

On average, one telephone call comes in every 30 seconds. It is known that
the number of telephone calls follows the Poisson distribution.

8.

(A)

(30, 60)

(B)

(4, 4)

(C)

(4, 16)

(D)

(8, 64)

(E)

(8, 8)

9.

10.

Three courses are offered to people of a company. Each person can take
only one course and the courses are open to people from other company as
well. Given the following data,
a. What is the probability of people from other company? (5%)
b. Randomly choose a person and find that he(she) is from other company.
What is the probability that he(she) takes course III?

 

11.

A random variable X follows the normal distribution with mean 200 and
standard deviation 25. The inspection rule of X is to reject the product if
the sample mean is greater than 210.
a. Write down the null and alternative hypothesis. (5%)
b. If a random sample of size 25 is selected, compute the probability of
type I error using the above decision rule. (5%)
c. If the real mean of X is 215 and the standard deviation is 25,
compute the probability of type II error using the same decision rule
and sample size. (5%)
d. If the sample size is 10, will the probability of type I error increase,
decrease, or stay the same as compared to (b)? Will the probability of
type II error increase, decrease, or stay the same as compared to (c)?
(5%)

12.