96年元智大學國際企業所統計學

1.

A variable contains five categories. It is expected that data are uniformly
distributed across these five categories. To test this, a sample of observed
data is gathered on this variable resulting in frequencies of 27, 30, 29, 21,
24. Using α = .01 , the degrees of freedom for this test are _______.

(A)

5

(B)

4

(C)

3

(D)

2

2.

A carload of steel rods has arrived at Cybermatic Construction Company.
The car contains 1,000 bundles of 50 rods each. Claude Ong, manager of
Quality Assurance, directs the receiving crew to deliver the 63th and 458th
bundles to his crew for 100% inspection. Claude randomly selected 63 and
458 from a table of random numbers. Claude’s sample of 100 rods is a
_______.

(A)

cluster sample

(B)

simple random sample

(C)

quota sample

(D)

systematic sample

3.

Of the last 100 customers entering a computer shop, 25 have purchased a
computer. If the classical method for computing probability that the next
customer will purchase a computer is

(A)

0.25

(B)

0.50

(C)

1.00

(D)

0.75

4.

In the textile industry, a manufacturer is interested in the number of
blemishes or flaws occurring in each 100 feet of material. The probability
distribution that has the greatest chance of applying to this situation is the
______.

(A)

normal distribution

(B)

binomial distribution

(C)

Poisson distribution

(D)

uniform distribution

5.

The key difference between the binomial and hypergeometric distribution
is that with the hypergeometric distribution ______.

(A)

the probability of success must be less than 0.5

(B)

the probability of success changes from trial to trial

(C)

the trials are independent of each other

(D)

the random variable is continuous

6.

f (x) = (1/10)e^{−x /10} , x ≥ 0 The mean of x is

(A)

0.10

(B)

1,000

(C)

100

(D)

10

7.

Doubling the size of the sample will _______

(A)

reduce the standard error of the mean to one-half its current value

(B)

reduce the standard error of the mean to approximately 70% of its
current value

(C)

have no effect on the standard error of the mean

(D)

double the standard error of the mean

8.

If a qualitative variable has 4 categories, how many dummy variables must
be created and used in the regression analysis?

(A)

3

(B)

4

(C)

5

(D)

6

9.

You want to build the regression model, the following scatter plot indicates
________.

(A)

a log x transform may be useful

(B)

a x² transform may be useful

(C)

a y² transform may be useful

(D)

no transform is needed

10.

You want to build the regression model, the following scatter plot indicates
_______.

(A)

no transform is needed

(B)

a log y transform may be useful

(C)

a x² transform may be useful

(D)

a log x transform may be useful

11.

The marketing department of a company has designed three different
boxes for its product. It wants to determine which box will produce the
largest amount of sales. Each box will be test marketed in five different
stores for a period of a month. Below you are given the information on
sales. (15%)

12.

In checking the reliability of a bank’s records, auditing firms sometimes
ask a sample of the bank’s customers to conform the accuracy of their
savings account balances as reported by the bank. Suppose an auditing
firm is interested in estimating the proportion of a bank’s savings account
on whose balances the bank and the customer disagree. Of 200 savings
account customers questioned by the auditors, 15 of them said their
balance disagreed with the reported by the bank. The bank claims that the
true fraction of accounts on which there is disagreement is at most 0.05;
You as an auditor, doubt this claim. Test the bank’s claim at a 0.10
significance level. (5%)

13.

Ron Jacobi, manager with the Toulee Department of Natural Resources, is
responsible for setting catch-and-release limits for Lake Norby, a large and
popular fishing lake. For the last two months he has been sampling to
determine whether the average length of Northern Pike in the lake exceeds
18 inches (using a significance level of 0.05). Assume that the P-value is
0.08. In concluding that the average size of the fish exceeds 18 inches,
Jacobi:

(A)

makes a Type II error

(B)

is correct

(C)

makes a Type I error

(D)

makes a power error

(E)

none of the above.

14.

(A)

0.36.

(B)

1.20.

(C)

2.57.

(D)

4.00

(E)

none of the above

15.

(A)

larger than 0.10.

(B)

between 0.10 and 0.05.

(C)

between 0.05 and 0.01.

(D)

below 0.01.

(E)

none of the above.

16.

To which of the following would it have been most important that the
subjects be blind during the experiment?

(A)

The identity of the sports writer.

(B)

The direction in which they were to kick the ball.

(C)

The method they were to use in kicking the ball.

(D)

Whether the ball they were kicking was filled with helium or air.

(E)

None of the above.

17.

If X and Y are perfectly correlated when you regress Y on to X you will find
that:

(A)

the alpha coefficient will be zero

(B)

the regression line will be sloped upward

(C)

the standard error of estimate will be zero

(D)

exactly half of the observations will plot above the regression line and
half will plot below the regression line

(E)

none of the above.

18.

A 90% confidence interval for the slope β_i in the simple linear regression
model is (approximately)

(A)

1.41 ± 0.57

(B)

1.41 ± 0.32

(C)

−1.41 ± 0.57

(D)

−1.41 ± 0.32

(E)

none of the above

19.

The correlation between mean assistant and full professor salaries is

(A)

0.055

(B)

0.355

(C)

0.596

(D)

0.772

(E)

none of the above

20.

Is there strong evidence (and if so, why) that the relationship between
mean assistant and full professor salaries is adequately described by a
straight line?

(A)

Yes, because the slope of the least-squares line is positive

(B)

Yes, because the P-value for testing if the slope is quite small

(C)

No, because the value of the square of the correlation is relatively small.

(D)

It is impossible to say, because we are not given the actual value of the
correlation

(E)

None of the above

21.

Here is a scatterplot of mean full versus assistant professor salaries (in
thousands of dollars)

Which of the following statements is supported by the plot?

(A)

There is no striking evidence in the plot that the assumptions for
regression are violated

(B)

There appears to be an outlier and/or influential observations in the
plot suggesting that our above results must be interpreted with caution

(C)

The plot contains dramatic evidence that the standard deviation of the
response about the true regression line is not even approximately the
same everywhere

(D)

The plot contains many fewer points than were used to fit the
least-squares regression line in the previous problems. Obviously there
is a major error present

(E)

None of the above.

22.

The value of MSE is

(A)

1.71

(B)

294

(C)

13813

(D)

15312

(E)

none of the above

23.

The proportion of the variation in the variable SAT-M that is explained by
the explanatory variables $ Per Pupil, % Taking, and Teacher’s Salary is

(A)

0.232

(B)

0.301

(C)

0.769

(D)

0.960

(E)

none of the above

24.

(A)

3.32

(B)

24.0

(C)

52.10

(D)

159.3

(E)

none of the above

A company runs a three-day workshop on strategies for working effectively in
teams. On each day a different strategy is presented. Forty-eight employees of
the company attend the workshop. At the outset, all 48 are divided into twelve
teams of four. The teams remain the same for the entire workshop. Strategies
are presented in the morning. In the afternoon, the teams are presented with a
series of small tasks, and the number completed successfully using the strategy
taught that morning is recorded for each team. The mean number of tasks
completed successfully by all teams each day and the standard deviation is
computed. The results are given below.

25.

The value of the ANOVA F statistic for this test is

(A)

0.0045

(B)

0.9988

(C)

1.0003

(D)

2.1479

(E)

none of the above

A company runs a three-day workshop on strategies for working effectively in
teams. On each day a different strategy is presented. Forty-eight employees of
the company attend the workshop. At the outset, all 48 are divided into twelve
teams of four. The teams remain the same for the entire workshop. Strategies
are presented in the morning. In the afternoon, the teams are presented with a
series of small tasks, and the number completed successfully using the strategy
taught that morning is recorded for each team. The mean number of tasks
completed successfully by all teams each day and the standard deviation is
computed. The results are given below.

26.

In this example, we notice

(A)

there is clear evidence of bias in the results. This is undoubtedly due to
the lack of blinding on the part of the subjects

(B)

the data show very strong evidence of a violation of the assumption that
the three populations have the same standard deviation

(C)

ANOVA cannot be used on these data because the sample sizes are less
than 20

(D)

the assumption that the data are independent for the three days in
unreasonable, because the same teams were observed each day

(E)

none of the above

A company runs a three-day workshop on strategies for working effectively in
teams. On each day a different strategy is presented. Forty-eight employees of
the company attend the workshop. At the outset, all 48 are divided into twelve
teams of four. The teams remain the same for the entire workshop. Strategies
are presented in the morning. In the afternoon, the teams are presented with a
series of small tasks, and the number completed successfully using the strategy
taught that morning is recorded for each team. The mean number of tasks
completed successfully by all teams each day and the standard deviation is
computed. The results are given below.

27.

For this example, which of the following conclusions is most reasonable?

(A)

There is moderate evidence that the strategies taught are effective in
increasing the number of tasks completed successfully for the first two
days, but then the effect appears to wear off

(B)

An ANOVA F test is not appropriate for these data. Instead, the
researchers should have done several tests to see if the number of tasks
completed successfully differed for the three days. This analysis would
have shown the treatment was effective

(C)

The data provide strong evidence that the mean number of tasks
completed successfully differ for the three strategies taught

(D)

The data appear to provide little or no evidence that the strategies
taught differ in their effectiveness in helping teams complete tasks
successfully

(E)

None of the above

28.