101年國立交通大學經營管理所統計學

Let X have the probability density function given by
f (x) = 2x , 0 < x < 1,
= 0 , elsewhere.
Then Pr(0 < X < 0.5) is

0.15

0.25

0.35

0.45

0.5

Let the random variable X of the discrete type have probabilities 0.125, 0.75, 0.125 at
the points −1 , 0, 1, respectively. Which of the following values is the least upper
bound of Pr(| X | ≥ 1) ?

0

0.0625

0.125

0.1875

0.25

Let U have a uniform (0, 12) distribution. Its probability density function is given by
g(u) = 1/12 , 0 < u < 12 , zero elsewhere. Then the variance of U is

6

9

12

15

18

Let U have a uniform (0, 12) distribution. Let F(x) be the distribution function of U.
Then F(3) is

0.15

0.25

0.35

0.5

0.75

When conducting a paired t test based on 10 observations, each of observations is
measured twice. The degrees of freedom of the paired t test is

9

10

18

19

20

Let pˆ for estimating the population proportion p be 0.5 based on a sample of size 100.
Then the estimated standard error of pˆ is

0.0025

0.005

0.025

0.05

0.25

If X and Y both have a standard normal distribution and X is independent of Y, then the
variance of X 2 + Y 2 is

1

2

4

6

8

Let X and Y be standardized random variables and X be independent of Y . Let
W = 0.8X + 0.6Y . Then the correlation coefficient between X and W is

0.8

0.6

0.64

0.36

0.48

Which of the following sampling distributions is used to test for goodness of fit?

the binomial distribution

the normal distribution

the t distribution

the χ 2 distribution

the F distribution

Which of the following sampling distributions is used to test if a correlation coefficient
is zero?

the binomial distribution

the normal distribution

the t distribution

the χ 2 distribution

the F distribution

A company that assembles memory boards for personal computers buys 60% of its
memory chips from supplier A and the remainder from supplier B. Supplier A produces
memory chips that are 5% defective, and B produces 10% defective. A memory chip is
selected randomly and a test of the chip shows that it is defective. What is the
probability that the chip was supplied by A?

0.03

0.05

0.43

0.57

0.6

Given that the population distribution of daily output on a production line for steel pipe
at Company A is normal and its standard deviation is σ = 10 tons. We want to estimate
the mean daily output of the production line, μ , to within ±2.5 tons with 95%
confidence. What sample size is required?

20

31

39

52

62

Consider a multiple regression with 3 independent variables based on 20 observations.
The degrees of freedom associated with the error in the ANOVA table is

15

16

17

18

19

Let X and Y have a trinomial distribution with 1 0.35 p1 = and 2 0.4 p2 = . Then the
correlation coefficient between X and Y is given by

0.14

-0.14

0.6

-0.6

0.75

Let S denote a sample space, and A and B be two events. Then

P(S) = 1

Pr(Y < 1) = 0.3

Pr(X < 1| Y < 1) = 0.2

Pr(Y = X | Y ≥ 1) = 0.5

Pr(X > 1) = 0.3

Pr(X = Y | X > 0) = 0.6

Let X have a Bernoulli distribution with p = 0.5 and Y have a Poisson distribution
with λ = 5 . Let X and Y be independent. Then

E(X −Y) = −4.5

E(2X −Y + 4) = 0

Var(2X ) = 1

Var(X − Y) = 5.25

Var(2X −Y + 4) = 10

Y is binomial (50, p)

Pr(Y = 1) = 50 p(1− p)49

Pr(Y = 50) = (1− p)50

Var(Y) = 50 p(1− p)

Y / 50 is approximately N( p, p(1− p)) .

E(Y | x) = x

E(Y | x) = 2x

E(X | y) = y

Var(Y | x) = 3

Var(Y | x) = 4

x2

(X1 + Xn ) / 2

Max{X1, X2 ,L, Xn}

Min{X1, X2 ,L, Xn}

X1, X2, ..., Xn are identically distributed.

X1, X2 ,..., Xn are independent.

the population distribution is approximately normal with mean μ and variance
σ 2 .

the population distribution is approximately N(0, 1) .

the sample variance is approximately normal.

Which of the following statements are correct regarding a test of 0 H against 1 H ?

Pr (critical region | 0 ) = H level of significance.

Pr (critical region | 1) = H power.

Pr (critical region | H0 ) = p -value.

Pr (acceptance region | 0 ) = H power.

Pr (acceptance region | H1) = p -value.

To test H0 :μ = μ0 versus H1 :μ ≠ μ0 for a normal population mean μ at the α
level of significance, use the following decision rules:

reject  H0 if the computed test statistic is located within the critical region.

reject  H0 if the p-value associated with the computed test statistic is less than
α / 2 .

reject H0 if the p-value associated with the computed test statistic is greater than
α .

reject  H0 if the  100(1- α)% confidence interval for μ includes μ0 .

reject  H0 if the  100(1- α)% confidence interval for μ does not include μ0 .

Which of the following statements are correct regarding the test of homogeneity and
the test of independence in two-way contingency table analysis?

Both of the tests have the same null hypothesis.

Both of the tests have the same test statistic.

Both of the tests have the same sampling distribution.

Both of the tests have the same sampling procedure.

Both of the tests are based on large samples.

Which of the following sampling distributions are used to test if a regression
coefficient is zero?

the binomial distribution

the normal distribution

the t distribution

the X2 distribution

the F distribution

The conditions that the least squares estimators are best linear unbiased estimators
(BLUE) in classical regression include

errors are independent.

errors are identically distributed.

errors are normally distributed.

sample regression coefficients are statistically significant.

coefficient of determination (R2 ) is large.

To test if error terms in the regression model are autocorrelated, use

the Durbin-Watson test

the Kolmogorov-Smirnov test

the Levene test

the Shapiro-Wilk test

the Wilcoxon test