IT IS CRITICAL TO NOTE THAT WHEN GIVEN THIS EXAM, STUDENTS WERE
EXPECTED TO USE THE TABLES TO FIND CRITICAL VALUES AND P-VALUES. WE
NO LONGER REQUIRE THIS, SO DON’T BE SPOOKED BY QUESTIONS THAT
INCORPORATE THAT COMPONENT. DESPITE THIS DRAWBACK, THE QUESTIONS
ARE REPRESENTATIVE OF THE KNOWLEDGE BASE AND TYPE OF QUESTIONS WE
TYPICALLY ASK. YOU SHOULD EXPECT TO SEE QUESTIONS WHICH UTILIZE
EXCEL OUTPUT IN YOUR MID-TERM.
ALSO NOTE THAT DUE TO THE VARIATION IN CHAPTER COVERAGE, THERE ARE
NO QUESTIONS ON THIS PRACTICE EXAM INVOLVING CHAPTER 17—THERE WILL
BE ON YOUR EXAM, AND THERE ARE NUMEROUS QUESTIONS DELETED AS THEY
WERE COVERING CHAPTERS THAT WE DID NOT INCLUDE THIS SEMESTER.
ANSWERS ARE INCLUDED FOR ALL QUESTIONS.
1.
If the value of the sample mean x is close enough to the hypothesized value of the
population mean  , then:
a. the hypothesized value is definitely true
b. the hypothesized value is definitely false
c. we reject the null hypothesis
d. we don’t reject the null hypothesis
ANSWER: d
2.
In testing the null hypothesis H 0 : p1  p2  0 , if H 0 is false, the test could lead to:
a. a Type I error
b. a Type II error
c. either a Type I or a Type II error
d. None of the above
ANSWER: b
4.
If we reject the null hypothesis, we conclude that :
a. there is enough statistical evidence to infer that the alternative hypothesis is true
b. there is not enough statistical evidence to infer that the alternative hypothesis is true
c. there is enough statistical evidence to infer that the null hypothesis is true
d. the test is statistically insignificant at whatever level of significance the test was
conducted at
ANSWER: a
5.
After testing the hypothesis below at the 5% significance level
H 0 :  2  .01
H 1 :  2  .01
given that a random sample of 10 observations was drawn from a normal population, and
the sample standard deviation was .043, you should conclude:
a. The Test Statistic = 2.334, and you should reject H0.
b. The Test Stastic = 2.334, and you should not rejet H0.
c. The Test Statistic = 1.664, and you should not reject H0.
d. The Test Statistic = 1.664, and you should reject H0.
ANSWER: d
7.
In testing the hypotheses
H 0 :   50
H1 :   50
the following information is known: n = 64, x = 53.5, and s = 10. The standardized test
statistic equals:
a. 1.96
b. –2.8
c. 2.8
d. –1.96
ANSWER: c
9.
There are three politicians who are attempting to win the Democratic nomination for
senator. In a survey of 1,000 Democrats, candidate A is favored by 550 people, candidate B
is supported by 300 people, and the remaining 150 respondents favor candidate C. If you
tested whether these results provide enough statistical evidence at the 1% significance level
to indicate that candidate A will receive at least 50% of the vote, the value of your Test
Statistic would be:
a. 3.16
b. –3.16
c. 2.84
d. –2.84
ANSWER: a
10.
Which of the following are measures of the linear relationship between two variables?
a. The covariance
b. The coefficient of correlation
c. The variance
d. Both a and b
ANSWER: d
12.
The Empirical Rule states that the approximate percentage of measurements in a data set
(providing that the data set has a bell-shaped distribution) that fall within two standard
deviations of their mean is approximately:
a. 68%
b. 75%
c. 95%
d. 99%
ANSWER: c
13.
In the formula x  z / 2 / n , the  / 2 refers to:
a. the probability that the confidence interval will contain the population mean
b. the probability that the confidence interval will not contain the population mean
c. the area in the lower tail or upper tail of the sampling distribution of the sample mean
d. the level of confidence
ANSWER: c
14.
Random samples from two normal populations produced the following statistics:
n1  10
n2  15
s12  32
s 22  22
In testing whether there is enough evidence at the 10% significance level to infer that the
variance of population 1 is different than the variance of population 2, your test statistic
value is:
a. 2.133
b. 0.6875
c. 1.50
d. 1.455
ANSWER: d
16.
An investor is considering two types of investment. She is satisfied that the
expected return on investment 1 is higher than the expected return on investment 2.
However, she is concerned that the risk associated with investment 1 is higher than that of
investment 2. To help make her decision, she randomly selects seven monthly returns on
investment 1 and ten monthly returns on investment 2. She finds that the sample variances
of investments 1 and 2 are 225 and 118, respectively. Can she infer at the 5% significance
level that the population variance of investment 1 exceeds that of investment 2?
a. No, they appear equal with a test statistic value of 1.907.
b. No, they appear unequal with a test statistic value of 1.907.
c. Yes, they appear equal with a test statistic value of 2.065.
d. Yes, they appear unequal with a test statistic value of 2.065.
ANSWER: a
17.
In constructing 95% confidence interval estimate for the difference between the means of
two normally distributed populations, where the unknown population variances are
assumed not to be equal, summary statistics computed from two independent samples are
as follows:
n1  50
x1  175
s1  18.5
n2  42
x2  158
s2  32.4
The upper confidence limit is:
a. 19.123
b. 28.212
c. 24.911
d. 5.788
ANSWER: b
22.
Generally speaking, if two variables are unrelated (as one increases, the other shows no
pattern), the covariance will be
a. a large positive number
b. a large negative number
c. a positive or negative number close to zero
d. none of the above
ANSWER: c
23.
A Type II error is defined as:
a. rejecting a true null hypothesis
b. rejecting a false null hypothesis
c. not rejecting a true null hypothesis
d. not rejecting a false null hypothesis
ANSWER: d
25.
In selecting the sample size to estimate the population proportion p, if we have no
knowledge of even the approximate values of the sample proportion p̂ , we:
a. take another sample and estimate p̂
b. take two more samples and find the average of their p̂
c. let p̂ = .50
d. let p̂ = .95
ANSWER: c
26.
Which of the following statements is true for the following data values: 7, 5, 6, 4, 7, 8, 12?
a. The mean, median and mode are all equal
b. Only the mean and median are equal
c. Only the mean and mode are equal
d. Only the median and mode are equal
ANSWER: a
28.
In testing the hypothesis
H 0 :   75
H 1 :  < 75
if the value of the test statistic equals –2.42, then the p-value is:
a. .5078
b. 2.420
c. .9922
d. .0078
ANSWER: d
29.
As the degrees of freedom for a t distribution increase, the t A value for a given tail area:
a. increases
b. approaches 1.0
c. approaches the z A value
d. approaches 0.
ANSWER: c
30.
In testing the hypotheses
H 0 : p  .40
H1 : p  .40
at the 5% significance level, if the sample proportion is .45, and the standard error of the
sample proportion is .035, the appropriate conclusion would be:
a. to reject H 0
b. not to reject H 0
c. to reject H 1
d. to reject both H 0 and H 1
ANSWER: b
31.
If some natural relationship exists between each pair of observations that provides a logical
reason to compare the first observation of sample 1 with the first observation of sample 2,
the second observation of sample 1 with the second observation of sample 2, and so on, the
samples are referred to as:
a. matched samples
b. independent samples
c. weighted samples
d. random samples
ANSWER: a
32.
In a given hypothesis test, the null hypothesis can be rejected at the .10 and .05 level of
significance, but cannot be rejected at the .01 level. The most accurate statement about the
p-value for this test is:
a. p-value = .01
b. p-value = .10
c. .01 < p-value < .05
d. .05 < p-value < .10
ANSWER: c
33.
A professor of statistics refutes the claim that the average student spends 3 hours studying
for the midterm exam. Which hypothesis is used to test the claim?
a. H 0 :   3
H1 :   3
b. H 0 :   3
H1 :   3
c. H 0 :   3
H1 :   3
d. H 0 :   3
H1 :   3
ANSWER: b
35.
A confidence interval is defined as:
a. a point estimate plus or minus a specific level of confidence
b. a lower and upper confidence limit associated with a specific level of confidence
c. an interval that has a 95% probability of containing the population parameter
d. a lower and upper confidence limit that has a 95% probability of containing the
population parameter
ANSWER: b
37.
Based on sample data, the 90% confidence interval limits for the population mean are
LCL = 170.86
UCL = 195.42.
If the 10% level of significance were used in testing the hypotheses
H 0 :   201
H1 :   201 ,
the null hypothesis:
a. would be rejected
b. would not be rejected
c. would have to be revised
d. None of the above
ANSWER: a
39.
Which of the following statements about the arithmetic mean is not always correct?
a. The sum of the deviations from the mean is zero
b. Half of the observations are on either side of the mean
c. The mean is a measure of the middle (center) of a distribution
d. The value of the mean times the number of observations equals the sum of all of the
observations
ANSWER: b
40.
In a hypothesis test for the population variance, the hypotheses are
H 0 :  2  30
H1 :  2  30 .
If the sample size is 20 and the test is being carried out at the 5% level of significance, the
null hypothesis will be rejected if:
a.  2  30.144
b.  2  10.851
c.  2  10.117
d.  2  31.410
ANSWER: c
41.
Which of the following is not a part of the formula for constructing a confidence interval
estimate of the population mean?
a. A point estimate of the population mean
b. The standard error of the sampling distribution of the sample mean
c. The confidence level
d. The value of the population mean
ANSWER: d
42.
The lower limit of a confidence interval at the 95% level of confidence for the population
proportion if a sample of size 200 had 40 successes is:
a. .2554
b. .1446
c. .2465
d. .1535
ANSWER: b
44.
In constructing a 90% interval estimate for the ratio of two population variances,  12 /  22 ,
two independent samples of sizes 40 and 60 are drawn from the populations. If the sample
variances are 515 and 920, then the lower confidence limit is:
a. .352
b. .341
c. .890
d. .918
ANSWER: a