Midterm—Form A
Summer 2002
Economics 173
Instructor: Petry
Name_____________
SSN______________
1. A descriptive measure of a population is called a(n)
a. parameter
b. mean
c. point estimator
d. statistic
e. interval estimator
ANSWER: A
2. A random sample of 400 university professors was taken. Each was asked the
following question: “What is your rank? (lecturer, assistant professor, associate
professor, full professor)”. Identify the type of data from the following options.
a. integer.
b. continuous.
c. qualitative.
d. quantitative.
e. all of the above.
ANSWER: C
Use the following information to answer the next 2 questions (#3 - 4).
After the 2000 Census, the distribution of income of the working population of
Champaign County between the ages 18 and 64 was constructed as shown as in the
following figure.
Distribution of Income
Income in dollars
3. This is an example of a
a. negatively skewed distribution.
b. positively skewed distribution.
c. symmetric distribution.
d. Both positively skewed and symmetric distribution.
e. Both negatively skewed and symmetric distribution.
ANSWER: B
4. If one were to place the mean, median and mode in order from the lowest number
to highest number for the above distribution, they would fall in the following
order:
a. mean, median, mode
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b.
c.
d.
e.
ANSWER: E
median, mean, mode
mode, mean, median
not enough information has been given to make a determination
none of the above.
Use the following information to answer the next 2 questions (#5 - 6).
A sample of data was collected on the number of businesses which went bankrupt in
12 major cities last month.
8, 10, 12, 32, 16, 10, 33, 11, 10, 18, 18, 9
5. The standard deviation of this data set is given by:
a. 12.0
b. 15.6
c. 8.6
d. 8.2
e. none of the above
ANSWER: C
6. The “rule of thumb” or “empirical rule” would state that:
a. effectively all of the data points should fall between –10.22 and 41.38
b. effectively all of the data points should fall between 8 and 33
c. approximately 68% of the data points should fall between –1.62 and 32.78
d. effectively all the data points should fall between 6.98 and 24.18
e. approximately 95% of the data points should fall between –10.22 and
41.38
ANSWER: A
Use the following information to answer the next 3 questions (#7 - 9).
Mark would like to test to see if the proportion of Economics students that study only
the night before the exam (population 1) is greater than the proportion of students that
study for at least two nights before the exam (population 2). Data was collected from
a sample of 100 students.
7. The proper test to run is:
a. t-test for difference in two means (population variance assumed equal)
b. t-test for difference in two means (population variance assumed unequal)
c. chi-square test for difference in two proportions
d. z-test for difference in two proportions
e. paired-sample t test
ANSWER: D
8. The appropriate alternative hypotheses for this problem is:
a. H1: p1 ≠ p2
b. H1: μ1 > μ2
c. H1: p1 > p2
d. H1: p1 = p2
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e. H1: μ1 ≠ μ2
ANSWER: C
9. If p1 was determined to be .48 and p2 was .52, and the test statistic was
determined to be -.5657, then which area represents the p-value for the specific
test described in the problem:
a.
b.
c.
d.
e.
ANSWER: D
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Use the following information to answer the next 2 questions (#10 - 11).
A new weight loss shake, Thin-Fast, is purported to decrease weight when combined with
exercise, more rapidly than exercise alone. To verify the claim, the FDA organized a test
with half of a group of 200 obese people being randomly assigned to the Thin-Fast and
Exercise Group (group #1), while the remainder were assigned to the Exercise Only
Group (group #2). Each person was weighed at the start of the regimen and four weeks
later, and the amount of weight lost was recorded (e.g. if person one lost 5 pounds, the
number 5 was entered).
10. In order to test whether Thin-Fast has made an accurate claim, what type of test
should be used:
a. z-test for difference in proportions
b. t-test for difference in means (variances unknown)
c. paired sample t-test
d. t-test for difference in means (variances known)
e. z-test for difference in means
ANSWER: B
11. What are the appropriate null and alternative hypotheses for this test:
a. H0: μ1 - μ2 = 0
H1: μ1 - μ2 ≠ 0
b. H0: μ1 - μ2 ≠ 0
H1: μ1 - μ2 = 0
c. H0: μ1 - μ2 < 0
H1: μ1 - μ2 > 0
d. H0: μ1 - μ2 = 0
H1: μ1 - μ2 > 0
e. H0: μ1 - μ2 = 0
H1: μ1 - μ2 < 0
ANSWER: D
12. In statistical inference, we:
a. make definitive statements about sample data, based upon as large a
sample size as possible
b. make probabilistic statements about sample data, using statistical
techniques
c. make probabilistic statements about population data, using sample data
d. make probabilistic statements about sample data, using population data
e. none of the above
ANSWER: C
13.
Which of the following statements regarding the p-value is true?
a. The p-value could be defined as the probability of observing a test statistic
less than the one computed given that the null hypothesis is false.
b. The p-value could be defined as the probability of committing a type I
error.
c. The p-value is found by first identifying the test statistic(s), then
calculating the area under the curve from that point(s) through the
rejection region(s).
d. The p-value could be defined as the amount of evidence in support of the
alternative hypothesis.
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e. both c and d are correct
ANSWER: E
14. The 90% confidence interval based on the sample mean X1 was determined to
be (12.65, 20.05). If one tests H0: μ = 18.30 and H1: μ ≠ 18.30 with a level of
significance of 5%, then one’s decision would be to:
a. Do Not Reject the null hypothesis and conclude that there is insufficient
evidence to conclude that the population mean is equal to 18.30.
b. Do Not Reject the null hypothesis and conclude there is insufficient
evidence to conclude that the population mean is not equal to 18.30.
c. Reject the null hypothesis and conclude that there is insufficient evidence
to conclude that the population mean is not equal to 18.30.
d. Reject the null hypothesis and conclude the population mean is 18.30.
e. None of the above.
ANSWER: B
15. If a person wants to test H0: μ1 - μ2 = 0 and H1: μ1 - μ2 ≠ 0 and σ1 and σ2 are
known then the appropriate test is:
a. t-test for difference in two means (population variance assumed equal)
b. t-test for difference in two means (population variance assumed unequal)
c. z-test for difference in two means
d. chi-square test for difference in two proportions
e. paired-sample t test
ANSWER: C
Use the following information to answer the next 3 questions (#16 - 18).
J&J
Mean
36.93333333
Variance
17.92380952
Observations
15
Pooled Variance
13.70245614
Hypothesized Mean Difference
0
df
t Stat
P(T<=t) one-tail
t Critical one-tail
1.685953066
P(T<=t) two-tail
4.4531E-05
t Critical two-tail
2.024394234
Eat-Fast
31.36
11.24
25
16. The type of test being conducted in this case must have been:
a. t-test for difference in two means (population variance assumed equal)
b. t-test for difference in two means (population variance assumed unequal)
c. z-test for difference in two means
d. F-test for ratio of variances
e. paired-sample t test
ANSWER: A
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17. The degrees of freedom for this test must have been:
a. 38
b. 40
c. 15, 25
d. 14, 24
e. none of the above
ANSWER: A
18. Assuming J&J was population 1, the test was being conducted to determine if
population parameter 1 was larger than population parameter 2 at a 1% level of
significance, the conclusion must have been:
a. Accept H0
b. Do Not Reject H0 in favor of the alternative
c. Reject H0 in favor of the alternative;
d. wait to make a decision later on
e. none of the above
ANSWER: C
Use the following information to answer the next 5 questions (#19 - 23).
The Chicago Bears football team would like to determine which Champaign-area
ambulance service to have on call in case of medical emergencies during home games for
the fall 2002 season. Two companies have made the final round. The principal criteria for
selecting between them is determined to be reaction time to recent 911 calls. The
response time for a random sample of 21 recent calls for each company (all of which
involve approximately the same physical distance) are recorded. The output for a variety
of tests involving this data are shown below.
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F-Test Two-Sample for Variances
Mean
Variance
Observations
df
F
P(F<=f) one-tail
F Critical one-tail
Professional
6.4
0.606
21
20
0.31819773
0.006848679
0.470775419
t-Test: Paired Two Sample for Means
Life-Line
6.004761905
1.90447619
21
20
Professional
Mean
6.4
Variance
0.606
Observations
21
Pearson Correlation -0.131248705
Hypothesized Mean Difference
0
df
t Stat
1.083861289
P(T<=t) one-tail
0.145660067
t Critical one-tail
1.724718004
P(T<=t) two-tail
0.291320134
t Critical two-tail
2.085962478
Life-Line
6.004761905
1.90447619
21
t-Test: Two-Sample Assuming Equal Variances
t-Test: Two-Sample Assuming Unequal Variances
Professional
Mean
6.4
Variance
0.606
Observations
21
Pooled Variance
1.255238095
Hypothesized Mean Difference 0
df
t Stat
1.143116232
P(T<=t) one-tail
0.12989304
t Critical one-tail
1.683852133
P(T<=t) two-tail
0.259786081
t Critical two-tail
2.021074579
Professional
Mean
6.4
Variance
0.606
Observations
21
Hypothesized Mean Difference
0
df
t Stat
1.143116232
P(T<=t) one-tail
0.130735329
t Critical one-tail
1.693888407
P(T<=t) two-tail
0.261470659
t Critical two-tail
2.036931619
Life-Line
6.004761905
1.90447619
21
Life-Line
6.004761905
1.90447619
21
19. If an F-test were appropriate, what would the value of the test statistic on the
right-hand side of that distribution be?
a. .3182
b. 1.084
c. 1.143
d. 3.143
e. none of the above
ANSWER: D
20. Assuming a two-tailed test for the difference in means was conducted, and a
5% significance level is used for any applicable tests, the appropriate p-value
to evaluate the difference in means hypothesis would be:
a. .2913
b. .2598
c. .2615
d. .0137
e. none of the above
ANSWER: C
21. If you were to place the three t-tests shown in numerical order depending
upon the number of degrees of freedom associated with each test (from lowest
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to highest), that order would be (use the following numbers to identify each
test):
1. t-test: paired two sample for means;
2. t-test: two-sample assuming equal variances;
3. t-test: two-sample assuming unequal variances
a. 1, 3, 2
b. 2, 3, 1
c. 3, 1, 2
d. 3, 2, 1
e. 2, 1, 3
ANSWER: A
22. Which of the following are measures of the linear relationship between two
variables?
a. covariance
b. coefficient of correlation
c. variance
d. both a and b
e. none of the above
ANSWER: D
23. Random samples from two normal populations produced the following statistics:
s12  32
n1  10
s 22  22
n2  15
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
e. 1.87
ANSWER: D
24. 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? You may assume:
F6,10,.975= .1831; F6,10,.95 = .2463; F6,10,.05 = 3.217; F6,10,.025 = 4.072;
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.
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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.
e. There is not enough information to make a determination.
ANSWER: A
25. In constructing a 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:
t.025,63=1.9983
n1  50
x1  175
s1  18.5
n2  42
x2  158
s2  32.4
The upper confidence limit is:
a. 19.1
b. 28.3
c. 24.9
d. 5.8
e. 8.6
ANSWER: b
26. 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. close to 1 or -1
e. none of the above
ANSWER: c
27. 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
e. combined samples
ANSWER: a
28. 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
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e. none of the above
ANSWER: c
29. 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
30. 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
31. 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
32. If two variables are strongly and positively correlated, the correlation coefficient
value will be close to:
a. 0.5
b. –0.5
c. a large but unknown negative number
d. 1.0
e. a large but unknown positive number
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ANSWER:
d
33. From a sample of 400 items, 14 are defective.
population proportion defective will be:
a. 14
b. 0.035
c. 28.57
d. .05-0.10
e. none of the above
ANSWER: b
The point estimate of the
Use the following information to answer the next 4 questions (#34 - 37).
The Manager of Armani’s Pizza is considering expanding to a new university town. He
believes that pizza sales is largely explained by the number of students enrolled at the
university where each of his restaurants is located. Enrollment at a new potential location
is 18.8 students (in thousands).
Armani's Pizza Sales & Student Enrollment
Restaurant
1
2
3
4
Sales*
42
56
31
14
Enrollment*
23
30
20
18
5
22
19
*Annual figures in thousands
34. The independent variable in this situation is:
a. sales
b. enrollment
c. number of stores
d. the manager’s shoe size
e. none of the above
ANSWER: B
35. He estimates the simple linear regression equation above, and finds the coefficient
for the independent variable to be:
a. 3.255
b. –38.617
c. 6.884
d. 4.669
e. 13.255
ANSWER: A
36. The estimate of the intercept coefficient is:
a. 3.255
b. -38.617
c. -16.884
d. 4.669
e. 13.255
ANSWER: B
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37. What should he expect his annual sales to be at the prospective new university
location?
a. –38.617
b. 61,194
c. 38,617
d. 32,553
e. 22,577
ANSWER: E
38. To test whether more than 60% of the UIUC students spend 50% or more of their
free time watching TV, your null hypothesis would be:
a. H0: p  0.50
b. H0: p  60
c. H0: p  0.60
d. H0: p =0.50
e. H0: p  0.60
ANSWER: C
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