Download Econ173_sp03MidtermAnswers

Midterm—Form A
Spring 2003
Economics 173
Instructor: Petry
Name_____________
SSN______________
Before beginning the exam, please verify that you have 10 pages with 35 questions in
your exam booklet. You should also have a decision-tree and formula sheet provided
by your TA. Please include your full name, social security number and Net-ID on
your bubble sheets. Good luck!
1. If a mound-shaped distribution is positively skewed, then the following is true:
a. median > mean > mode
b. mode < median < mode
c. median < mode <mean
d. mode < median < mean
e. mode > mean > mode
2. Econ 173 midterm exam was graded and the mean grade was 70% with a standard
deviation of 10%. Using the empirical rule, determine what proportion of grades were
either higher than 90% or lower than 60%.
a. 18.5%
b. 21%
c. 32%
d. 34.5%
e. 37%
3. Based on the following data, find the correlation coefficient.
Data set 1: 5, 7, 9, -1, 15, 8, 14
Data set 2: 9, 14, 8, 0, 17, 10, 4
a. 16.85714
b. 0.017431
c. 0.542061
d. 0.464624
e. 2.861243
4. Based on the same data as above, calculate the covariance.
a. 16.85714
b. 0.017431
c. 0.542061
d. 0.464624
e. 2.861243
5. Suppose you want to test whether the mean weight of all UIUC students is 150 lbs, and
you obtain a sample of 150 students. A point estimate for this test would be:
a. sample variance
b. population variance
c. population mean
d. sample mean
e. sample standard deviation
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6. Suppose that you are a quality control manager for Kraft and you receive a complaint
that Alfredo Cheese Jars are under-filled. You want to be 95% sure that the filling
machine is filling jars within 0.2 oz of the mean. Assume that previous studies suggest
that the population is normally distributed with population standard deviation of 0.9. How
big of a sample do you need to conduct this test? (z0.025=1.96, z0.05=1.645, z0.1=1.28)
a. 40
b. 9
c. 34
d. 77
e. 78
Use the following information to answer the next two questions (#7-8).
Prof. Petry believes that fewer students are showing up for his Econ 173 lectures this
year, compared to past years. Historically, each Econ 173 lecture is attended by 125
students on average. He gives you an assignment to test his claim that this years’s
average is lower than the historical average. You therefore record attendance for a
random sample of this year’s lectures. This gives you 40 sample observations with a
mean of 120 and a standard deviation of 10.
7. You null and alternative hypotheses are:
a. H0: μ≥0; H1: μ<0
b. H0: μ≥125; H1: μ<125
c. H0: μ≤0; H1: μ>0
d. H0: μ≤125; H1: μ>125
e. H0: μ<125; H1: μ≥125
8. What can you say about the test statistic?
If follows a _____________ distribution and the value of the test statistic is ___________
a. standard normal, -3.16228
b. χ2, 75.89466
c. t, -3.16228
d. Z, -0.31623
e. t, 3.16228
9. Suppose that you have constructed a 90% confidence interval for the population mean
using a sample of 50 observations. Moreover, suppose that the width of the confidence
interval is too large for your taste and you would like to decrease it. What would you do
(to be definitely sure of width reduction, and utilizing only the information provided
here)?
a. increase the sample size to 60 and increase the confidence interval to 95%.
b. decrease the sample size to 40 and increase the confidence interval to 95%.
c. decrease the sample size to 40 and decrease the confidence interval to 85%
d. increase the sample size to 60 and decrease the confidence interval to 85%
e. none of the above.
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10. Construct a 95% confidence interval for the population mean using the following
sample information. You have 24 observations and the mean of the observations is 34
while the sample standard deviations is 15. (Z0.025=1.96, Z0.05=1.645, Z0.1=1.28, t0.025,
33=2.51, t0.05, 33=2.03, t0.1, 33=1.71)
a. [27.999, 40.001]
b. [28.764, 39.236]
c. [27.784, 40.216]
d. [28.963, 39.037]
e. [26.315, 41.685]
11. Suppose you want to test whether more than 50% of the UIUC students are taller than
5’3” (63 inches). What would your null and alternative hypotheses be?
a. H0: μ≥63; H1: μ<63
b. H0: p≥0.5; H1: p<0.5
c. H0: μ≤63; H1: μ>63
d. H0: p≤0.5; H1: p>0.5
e. H0: μ<0.5; H1: μ≥0.5
12. In simple linear regression, the “best” line through the data points is fitted by:
a. minimizing the sum of the distances between the points and the line
b. minimizing the sum of the squared distances between the points and the line
c. maximizing the sum of the distances between the points and the line
d. maximizing the sum of the squared distances between the points and the line
e. the time honored trial and error method
Use the following information to answer the next two questions (#13-14).

x  36

y  54
cov(x,y) = 22
s
2
x
 14
13. Calculate the regression slope. It is:
a. 88.36
b. 0.11
c. 1.57
d. -2.57
e. cannot be calculated from the given information
14. Calculate the regression intercept. It is:
a. 88.36
b. 0.11
c. 1.57
d. -2.57
e. cannot be calculated from the given information
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Use the following information to answer the next six questions (#15-20).
The following regression output is generated from a study of ice cream sales (in
thousands of dollars) as the y-variable and daily high temperature (in degrees Farenheit)
as the x-variable.
Regression Statistics
Multiple R
0.960702626
R Square
Adjusted R
Square
0.915944948
Standard Error
Observations
13
ANOVA
df
Regression
Residual
Total
Intercept
Degrees
1
11
12
SS
2.312911537
0.193088463
2.506
MS
2.312912
0.017553
F
131.7636
Coefficients
9.444774028
0.094927623
Standard Error
0.288547963
0.008269798
t Stat
32.73208
P-value
2.58E-12
1.83E-07
Significance
F
Lower 95%
8.809683922
0.076725911
Upper
95%
10.07986
0.113129
15. The coefficient of determination in this case is:
a. 0.923
b. 0.411
c. 1.023
d. 0.271
e. cannot be determined based on the information provided
16. The coefficient of determination is a measure of:
a. the proportion of variability in the independent variable explained by the variation
in the dependent variable.
b. the proportion of variability in the dependent variable explained by the variation
in the independent variable.
c. the proportion of variability in the test statistic explained by the variation in the
dependent variable.
d. the proportion of variability in the p-value explained by the variation in the
dependent variable.
e. none of the above.
17. The standard error of the estimate in this case is:
a. 0.369
b. 0.301
c. 0.767
d. 0.132
e. cannot be determined based on the information provided
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18. The value of the test statistic for testing the null hypothesis that the regression slope is
insignificant is:
a. 32.732
b. 0.0008
c. 11.479
d. 5.045
e. cannot be determined based on the information provided
19. The p-value for testing the null against the alternative hypothesis that the population
slope is strictly greater than zero is:
a. 1.83E-07
b. (1.83E-07)*0.5
c. 1 - (1.83E-07)*0.5
d. 2.58E-12
e. cannot be determined based on the information provided
20. Based on this output, which of the following statements is true?
a. for every one degree rise in temperature, ice cream sales increase by about 95
dollars.
b. for every one degree rise in temperature, ice cream sales decrease by about 95
dollars.
c. to achieve a thousand dollar rise in sales, the temperature must rise by about 0.095
degrees.
d. to achieve a thousand dollar rise in sales, the temperature must fall by about 0.095
degrees.
e. for every one degree rise in temperature, ice cream sales decrease by about 0.095
dollars.
Use the following information to answer the next five questions (#21-25).
Murphy Lee claims that Foot Locker (population 1) is more expensive than Nike Town
(population 2). To test his claim, he takes a sample of 20 randomly selected shoes from
each store and computes its average price. The mean shoe price at Foot Locker is $84.11
with a standard deviation of 7.04, and the mean shoe price at Nike Town is $99.20 with a
standard deviation of 10.49. Assume the population variances are equal.
Also note the following critical values:
t 0.025,19  2.445
t 0.05,19  2.10
z 0.025  1.96
t 0.025,38  2.334
t 0.05,38  2.024
z 0.05  1.645
21. Which of the following statements is TRUE?
a. the hypotheses for this test are Ho: μ1-μ2=0 and H1: μ1- μ2≠0
b. a t test assuming equal variances cannot be performed because the sample
variances are not equal.
c. the degrees of freedom for this test are 19
d. the pooled variance is approximately equal to 8.933
e. none of the above.
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22. The point estimate and test statistic for this test are respectively:
a. -15.09 and -5.34177
b. 15.09 and -5.34177
c. 5.34177 and –15.09
d. -5.34177 and -15.09
e. there is not enough information given to compute the test statistic
23. The correct formula in Excel to compute the p-value for this test is:
a. =NORMSDIST(-15.09, 19, 2)
b. =CHIDIST(-5.34177, 38, 2)
c. =TDIST(5.34177, 38, 1)
d. =TDIST(-5.34177, 19, 2)
e. =NORMSDIST(15.09, 19, 1)
24. The conclusion for this test at a 5% level of significance is:
a. reject the null hypothesis
b. do not reject the null hypothesis
c. not enough information is available to complete the test
d. the test proves inconclusive
25. The 90% confidence interval for the population mean difference is:
a. 9.371, 20.808
b. -19.853, -10.327
c. 9.177, 21.003
d. –20.808, -9.372
e. –15.09, 15.09
26. In performing a Ratio of Two Variances test, which of the following statements is
TRUE?
a. the test uses the ratio of one sample variance over the other to do the analysis.
b. the test is used in a variety of situations where the variances are of direct interest.
c. the test is used to determine which difference in means test to use (equal or
unequal variances test) when given independent samples.
d. the test statistic follows an F distribution.
e. all of the above.
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Use the following information to answer the next three questions (#27-29).
Kaplan, a test preparation company, claims that it can, on average, improve student ACT
scores by more than 2 points through their comprehensive training program. To test their
claim, a competitor took a sample of 20 students and recorded their ACT score before
and after the Kaplan course. Consider “After Kaplan” population 1, and “Before Kaplan”
population 2. The Excel output is given below.
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean Difference
Df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
Before
After Kaplan
Kaplan
25.6
24.15
23.93684211 34.13421053
20
20
0.96151244
2
19
-1.39640882
0.08934639
1.729131327
0.17869278
2.093024705
27. Which test is appropriate for this problem?
a. a t-test for difference in two means assuming equal variances.
b. a t-test for difference in two means assuming unequal variances
c. a paired sample t-test
d. a Z test for the difference of two proportions
e. none of the above.
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28. Which shaded area (designated by the arrow) is the appropriate p-value for the
following test?
a.
b.
c.
d.
e.
29. What is your conclusion for this test, at a 10% level of confidence?
a. H1: μd≠0
b. Ho: μd=0
c. Ho: μd=2
d. H1: μd>2
e. Ho: μd<2
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30. A 94% Confidence Interval for the population mean is given as: [-0.98, 2.44]. You
need to perform a test on the population mean, where the alternative hypothesis is: H1:
µ≠0, at the 5% significance level. You would:
a. reject the null hypothesis
b. not reject the null hypothesis
c. be forced to change your alternative hypothesis
d. be forced to change your null hypothesis
e. remain inconclusive, as the test cannot be performed due to inadequate
information.
31. A 94% Confidence Interval for the population mean is given as: [-0.98, 2.44]. You
need to perform a test on the population mean, where the alternative hypothesis is: H1:
µ≠0, at the 10% significance level. You would:
a. reject the null hypothesis
b. not reject the null hypothesis
c. be forced to change your alternative hypothesis
d. be forced to change your null hypothesis
e. remain inconclusive, as the test cannot be performed due to inadequate
information.
32. MTV India is the premium cable music channel in the subcontinent. Before launching
their new classic rock based show, they would like to test the popularity of the band Pink
Floyd (as a representative band) in two of their markets, namely Peshawar (Pakistan) and
Dhaka (Bangladesh). In Peshawar, 12 out of 620 people quizzed had heard Pink Floyd. In
Dhaka, 477 out of 729 people recognized the band.
Based on this data, the appropriate test to use to test if classic rock is more popular in
Dhaka than in Peshawar is:
a. chi square test
b. t-test for difference in means
c. z-test for difference in means
d. z-test for difference in proportions
e. F-test for variances
33. In order to select the correct t-test for a difference in means question, which
preliminary test may need to be performed?
a. chi square test
b. t-test for difference in means
c. z-test for difference in means
d. z-test for difference in proportions
e. F-test for variances
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34. Suppose you are the manager of a chain of pizza restaurants. You would like to know
if the restaurant in Champaign is more or less profitable than the restaurant in Urbana.
You gather daily profit data (measured in dollars) from both stores for a six-month period
from March until August. Suppose that both stores are located on campus and are thus
affected by the number of students on campus. Given this information, which of the
following tests would be most appropriate to use to test whether one store is more
profitable than the other?
a. chi square test
b. t-test for difference in means
c. z-test for difference in means
d. z-test for difference in proportions
e. F-test for variances
35. Suppose you are the manager of a chain of pizza restaurants. You would like to know
if the restaurant in Champaign has larger fluctuations in profit than does the Urbana
restaurant. You gather daily profit data (measured in dollars) from both stores for a sixmonth period from March until August. Given this information, which of the following
tests would be most appropriate?
a. chi square test
b. t-test for difference in means
c. z-test for difference in means
d. z-test for difference in proportions
e. F-test for variances
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