Midterm—Sample
Fall 2001
1.
Economics 173
Instructor: Petry
Name_____________
SSN______________
Given the following t-statistics (23 degrees of freedom) and p-values (1 tailed);
t-statistic: 1.7  p-value .05
t-statistic: 1.2  p-value .121
t-statistic: 2.1  p-value .023
What is the p-value for the t-statistic 1.3?
a.
b.
c.
d.
e.
.141
.103
.042
.013
.461
2.
When comparing the proportions of two populations, what type of test statistic is
used?
a.
b.
c.
d.
e.
z
t
F
all of the above
none of the above
3.
Given a population standard deviation of 13, a sample mean of 40, and a
confidence interval width of 10, and a critical value of 1.645, what is the sample size?
a.
b.
c.
d.
e.
4.
If the p-value for a test is .4 then your decision is:
a.
b.
c.
d.
e.
5.
4
5
6
7
8
there is sufficient evidence to conclude the alternative is correct.
there is sufficient evidence to conclude the null is correct.
there is insufficient evidence to conclude the alternative is correct.
there is insufficient evidence to conclude neither is correct.
none of the above
Which of the following statements are equivalent?
I.
Alpha
II.
Beta
III.
Probability of a Type I error
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IV.
V.
a.
b.
c.
d.
e.
Probability of a Type II error
Probability of Rejecting a true null
I and IV
I and III
I and III and V
II and V
II and IV and V
6.
The 95% confidence interval for the population average final exam score is
[126.4, 195.5]. To test the claim that the average final exam score of the population is
180 at a 3% level of significance, what will be your decision?
a.
b.
c.
d.
e.
reject the null – conclude it is not 180
fail to reject the null – insufficient evidence to conclude it is not 180
reject the null – conclude it is 180
fail to reject the null – sufficient evidence to conclude it is not 180
cannot decide based on the given information
7.
When doing a matched pairs test with differences distributed normally and
unknown population standard deviation, which is the correct test statistic?
a. equal variances pooled t test for means
b. unequal variances pooled t test for means
c. single population means test on the difference
d. none of the above
e. any of the above will work
8.
If you wish to know if more than 45% of the class scored above 70% on the exam,
what is your null hypothosis?
a.
b.
c.
d.
e.
H0: p=0.7
H0: p=0.45
H0: p>0.7
H0: p>0.45
any of the above will work
9.
Suppose we are interested in whether the mean scores on the midterm for
Economics 173 is below 80%. Given a p-value of .11 what is your conclusion?
a.
b.
c.
d.
e.
fail to reject the null at any reasonable level of significance
cannot determine based on the given information
reject the null at any reasonable level of significance
fail to reject the null only if the significance level is .01
reject the null only if the significance level is .01
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10.
Given the following list of observations: 1, 10, 34, 15, 8, 40, 90, 41, 5, 16. What
proportion is above 8?
a.
b.
c.
d.
e.
.4
.5
.6
.7
.8
11.
Before running an equal variances pooled t-test, what test should you run to
formally decide if the needed assumptions are correct?
a.
b.
c.
d.
e.
F-test for variances
t-test for variances
z-test for variances
no need to run a test
eyeball test
12.
A pharmaceutical company currently produces an anesthetic whose effective time
is normally distributed with mean 7.4 and standard deviation 1.2. It is considering the
launch of a new drug that they believe has a lower mean effective time but the same
standard deviation. In a clinical study meant to test their belief, what would be the
appropriate null and alternative hypothesis?
Ho:  > = 7.4, H1:  < 7.4
Ho:  > 7.4, H1:  < =7.4
Ho:  = 7.4, H1:   7.4
Ho:  < = 7.4, H1:  > 7.4
a.
b.
c.
d.
13.
Irrespective of your answer in the last question suppose that you intend to do a
two-sided test. You collect a sample and compute the sample mean. In order to reject the
null hypothesis at a 10% level of significance, using a Z statistic of 1.645, and a sample
size of 25,
a.
b.
c.
d.
you need the sample mean to be smaller than 7.01
you need the sample mean to be greater than 7.79
both of the above
none of the above
14.
The mean of a sample is computed to be –0.301. It has been found out that the pvalue is 0.275 when testing Ho:  = 0 against the two sided alternative H1:   0. To test
Ho:  = 0 against the one sided alternative H1:  < 0 at a significance level of 0.5, we
will have:
a. a p-value of 0.275 and therefore reject the null hypothesis
b. a p-value of 0.138 and therefore reject the null hypothesis
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c. a p-value of 0.862 and therefore accept the null hypothesis
d. a p-value of 0.5 and therefore the test results will be inconclusive.
15.
The following table presents the summary statistics from a sample of 24 exam
scores, expressed in percentages.
Score
Mean
Standard Error
Median
Mode
Standard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
Confidence Level(95.0%)
75.66667
1.782226
73
73
8.731087
76.23188
0.646501
1.303676
30
66
96
1816
24
3.68681
In order to do a test where the null hypothesis specifies the population mean to be
equal to 70,
a.
b.
c.
d.
the t-distribution should be used to get a test statistic equal to 3.18
the z-distribution should be used to get a test statistic equal to 3.18
not enough information is given to calculate the test statistic
a pooled variance t-test should be used
16.
Based on a 95 % confidence interval, if you tested Ho:  = 70, H1:   70, you
would:
a.
b.
c.
d.
17.
not be able construct the confidence interval due to lack of information.
Accept the null hypothesis
Reject the null hypothesis
Reformulate a one sided hypothesis instead.
The pooled variance t-test is based on the following assumption(s):
a.
b.
c.
d.
that the two populations be independent
that the two populations have approximately equal variances
that both populations be normal
all of the above
18.
A truck manufacturer has two plants, one in Champaign and one in Urbana. The
CEO of this company suspects that the Urbana plant is more efficient (in terms of number
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of trucks produced each month) than the Champaign one. Let Champaign be plant 1 and
Urbana be plant 2 . Then the test should be specified as:
a.
b.
c.
d.
H0: 1-2 = 0, H1: 1-2  0
H0: 1-2 = 0, H1: 1-2 < 0
H0: 1-2 = 0, H1: 1-2 > 0
H0: 1-2 < 0, H1: 1-2 > 0
19.
For the scenario described above, monthly production data was collected from
both plants for a year and a pooled variance t-test was performed at the 5% significance
level. The results of the test are presented below.
Mean
Variance
Observations
Pooled Variance
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
CHAMPAIGN
URBANA
57.75 55.66667
5.840909091 13.15152
12
12
9.496212121
0
22
1.655995622
0.055959227
1.717144187
0.111918455
2.073875294
Based on the correct answer to the last question,
a.
b.
c.
d.
20.
The p-value is 0.056 so we do not reject the null hypothesis
The p-value is 0.112 so we do not reject the null hypothesis
The p-value is 0.888 so we do not reject the null hypothesis
The p-value is 0.944 so we do not reject the null hypothesis.
The test for difference in proportions between two populations uses
a.
b.
c.
d.
the z-distribution
the f-distribution
the t-distribution
both a and b
21.
Suppose a record store chain (Badidea cd’s) is running a promotion for the new
Grand Funk Railroad anthology that was released last summer. Badidea cd’s would like
to know whether or not the promotion that it ran was successful or not based on it’s own
sales (23 stores) of the anthology before and after the promotion. In order to test this
hypothesis which of the following tests should be used?
a. pooled variance t-test assuming equal variances
b. pooled variance t-test assuming unequal variances
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c. paired sample t-test
d. z test for difference in means
e. z test for difference in proportions
22.
Suppose two record store chains are both running a promotion for the re-release
of Mike and the Mechanics Reggae Christmas album that was released last August.
Badidea cd’s (23 stores) would like to know if it’s store sold a significant amount more
than its competition Dave’s Unbelievable Music Bin (DUMB) (18 stores). In order to
test this which of the following tests would be the most appropriate?
a.
b.
c.
d.
e.
pooled variance t-test assuming equal variances
F test for difference in variance
z test for difference in proportions
t-test for population mean
paired sample t-test
23.
A poll was taken recently on the UI campus asking students whether or not they
support military action to solve world conflict. Suppose you believe that men and
women answer this question differently. In order to test your hypothesis that men would
answer “Yes, I support military action” more often that women, which of the following
tests could you perform?
a.
b.
c.
d.
e.
pooled variance t-test assuming equal variances
pooled variance t-test assuming unequal variances
paired sample t-test
z test for difference in means
z test for difference in proportions
24.
A poll was taken recently on the UI campus asking students whether or not they
support military action to solve world conflict. Suppose you believe that the percentage
of students who support military action is more than half. In order to test this hypothesis
which of the following tests could you perform?
a.
b.
c.
d.
e.
z test for difference in proportions
t-test for population mean
F test for difference in variance
z test for population proportion
pooled variance t-test assuming equal variances
25.
A professor studying “grade inflation” (the upward trend in letter grades in most
college courses) believes that the upward trend in grades is accompanied by a greater
uncertainty (ie wider dispersion or spread) of letter grades. To test whether or not there is
more uncertainty in letter grades, which of the following tests could be performed?
a. z test for difference in proportions
b. t-test for population mean
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c. F test for difference in variance
d. z test for population proportion
e. pooled variance t-test assuming equal variances
26.
In the simple linear regression model, the intercept and slope coefficients are
computed by minimizing,
a. SSE
b. the sum of the squared discrepancies between the observed values and its
conditional mean
c. the sum of the squared discrepancies between the predicted values and the
conditional means
d. both a and b
e. both b and c
Use the following Excel output to answer the following questions. (Note: some
parts left blank)
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.164737873
R Square
0.027138567
Adjusted R Square
0.017109068
Standard Error
6.982167345
Observations
99
ANOVA
df
Regression
Residual
Total
Intercept
X Variable 1
27.
1
97
SS
MS
F
Significance F
131.9131721 131.9131721 2.705874543 0.103216227
4860.727273
Coefficients Standard Error
t Stat
P-value
10.00368557 0.872243025 11.46892012 9.40437E-20
-0.231771626 0.140898523 -1.644954268 0.103216227
Lower 95%
8.272525588
-0.511416034
Based on the Excel output what is the value for the total degrees of freedom?
a.
b.
c.
d.
e.
99
98
1
97
0
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28.
Based on the Excel output what is the value of MSE?
a.
b.
c.
d.
e.
4728.81
4992.64
48.75
356.94
not enough information to answer
29.
Based on the Excel output what is the correct interpretation for the slope
coefficient?
a.
b.
c.
d.
e.
For every 1-unit change in X, the expected average change in Y is –0.23 units.
For every 1-unit increase in X, the expected average change in Y is –0.23 units.
For every 1-unit increase in X, the expected average change in Y is 10.00 units.
For every –0.23 unit decrease in X, the expected average change in Y is 1 unit.
For every 1-unit increase in Y, the expected average change in X is –0.23 units.
30.
Based on the Excel output what is the value of the appropriate test statistic for
testing whether or not X has a significant effect on Y?
a.
b.
c.
d.
e.
31.
Calculate the mean of the following array: 20 24 29 54 65 78
a.
b.
c.
d.
e.
32.
40
45
50
55
65
What is the median salary of the following array: 20 24 29 54 65 78
a.
b.
c.
d.
e.
33.
11.47
–1.64
0.027
0.103
none of the above
29
38
41.5
46.7
66
If the distribution is symmetrical, which of the following are equivalent?
a. the mean and median
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b.
c.
d.
e.
34.
the mode and the median
the mean and the mode
the mean, the mode, and the median
none of the above
The range of the measurements is:
a.
b.
c.
d.
e.
35.
the difference between the smallest and largest measurements
the test statistic as measured in Excel
the average of all measurements
the number of measurements
the difference between the mean and the test statistic
The variance is:
a.
b.
c.
d.
e.
36.
2 times the standard deviation
the square root of the standard deviation
the absolute value of the standard deviation
the standard deviation squared
none of the above
Find the variance (in years) of the following array: 3.4, 2.5, 4.1, 1.2, 2.8, 3.7
a.
b.
c.
d.
e.
37.
1
1.05
1.275
2.95
1.075
Which of the following are true regarding the standard deviation:
a.
b.
c.
d.
e.
38.
can be used to compare the variability of several distributions
make a statement about the shape of the distribution
contains 68% of the measurements within 1 and –1 standard deviations
contains 95% of the measurements within 2 and –2 standard deviations
all of the above
Covariance determines:
a.
b.
c.
d.
e.
the strength of the linear relationship between two variables
if there is any pattern to the way the two variables move together
the shape of the distribution
the size of the population being measured
both a and b.
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39.
If two variables are strongly and positively correlated, the coefficient value will
be close to:
a.
b.
c.
d.
e.
0
.5
–1
1
.2
40.
What is the 95% confidence interval (Z= 1.96), for a mean of 7.8, a population
standard deviation of 3, and a sample of 85:
a.
b.
c.
d.
e.
41.
7.0651, 8.5554
7.1622, 8.4377
6.9749, 7.8846
7.2432, 8.5094
7.2321, 8.6858
The width of the interval estimator is a function of:
a.
b.
c.
d.
e.
42.
the population standard deviation
the sample size
the confidence level
all of the above
none of the above
Increasing the sample size:
a.
b.
c.
d.
e.
decreases the width of the interval estimator
increases the width of the interval estimator
changes the confidence interval
leads to exactly the same standard deviation
none of the above
43.
What sample size is required for a machine to be precise within 1 inch with 95%
confidence (Z = 1.96)? Assume population is normally distributed, with a population
standard deviation of 4.
a.
b.
c.
d.
e.
120
62
61
70
59
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Answer Key:
1.
b
2.
a
3.
b
4.
c
5.
c
6.
b
7.
c
8.
b
9.
a
10.
d
11.
a
12.
a
13.
c
14.
b
15.
a
16.
c
17.
d
18.
b
19.
d
20.
a
21.
c
22.
a
23.
e
24.
d
25.
c
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26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
d
b
c
b
b
b
c
d
a
d
e
e
b
d
b
d
a
b
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