252x0622 11/08/06 (Page layout view!)
ECO252 QBA2
Name Corrections
SECOND HOUR EXAM Circle Hour of Class Registered
November 8, 2006
MWF2, MWF3, TR12:30, TR2
Show your work! Make Diagrams! Exam is normed on 50 points. Answers without reasons are not
usually acceptable.
I. (8 points) Do all the following. Make diagrams!
x ~ N 19, 9 - If you are not using the supplement table, make sure that I know it.
1. P10  x  35 
2. Px  2
3. P0  x  19 .00 
4.
x.065
252x0622 11/08/06
II. (22+ points) Do all the following? (2points each unless noted otherwise). Look them over first – the
Note the following:
1. This test is normed on 50 points, but there are more points possible including the take-home.
You are unlikely to finish the exam and might want to skip some questions.
2. A table identifying methods for comparing 2 samples is at the end of the exam.
3. If you answer ‘None of the above’ in any question, you should provide an alternative
answer and explain why. You may receive credit for this even if you are wrong.
4. Use a 5% significance level unless the question says otherwise.
5. Read problems carefully. A problem that looks like a problem on another exam may be
quite different.
computer problem is at the end.
1.
A company gives an exam to graduates of quality control programs in two plants samples of scores
are as follows:
Boston 78 82 66 69 85
Atlanta 50 66 69 85
a. Compute the sample variance for Boston – Show your work! The sample mean and standard deviation
for Atlanta are 67.50 and 14.34. (2)
b. Is there a significant difference between the scores in the two plants? You may assume that variances are
equal. State your hypotheses! (2)
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252x0622 11/08/06
Exhibit 1
The director of the MBA program of a state university wanted to know if a year of MBA work would
change the proportion among potential students who would perceive the program as being good. A
random sample of 215 incoming students is compared with a random sample of 215 second-year
students. Of the first group 164 students viewed the program as ‘good.’ Of second year students 130
viewed the program as ‘good.’ She wishes to see if the fraction that considered the program ‘good’ has
fallen.
2.
Referring to Exhibit 1, which test should she use? (2)
2
a)  -test for difference in proportions
b) Z-test for difference in proportions
c) McNemar test for difference in proportions
d) Wilcoxon rank sum test
3.
Referring to Exhibit 1, what is the null hypothesis? (2)
4.
Referring to Exhibit 1, what is the value of the computed test statistic? (4)
[12]
5.
Referring to Table Exhibit 1, what is the p-value of the test statistic?(2)
[8]
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252x0622 11/08/06
Exhibit 2
(Dummeldinger) A researcher took a random sample of n graduates of MBA programs, which included
n1 women and n 2 men. Their starting salaries were recorded. Use 1 and/or  1 for population parameters
for women and  2 and/or  2 for men.   .10  The sample yields following data.
x 2  50200 .00
s 2  13557 .29
x1  48266 .70
s1  15678 .01
and
. n1  n 2  200 . The researcher wants to show that men have a higher mean starting salary
than women. Assume that these are independent samples. Hint: To preserve both our sanity, move the
decimal point three places to the right in both the means and standard deviations. You will be
working in thousands but will get the same value for the test ratio.
We want to see if the means or medians, as appropriate, are different.
Assume that these are independent samples from population with a Normal distribution and that  12   22 .
6.
Referring to Exhibit 2, if D  1   2 what is the null hypothesis? (1)
a) D  0
b) D  0
c) D  0
d) D  0
e) D  0
f) None of the above. (Give the correct one!)
7.
Referring to Exhibit 2, if we do not have a computer available, which of the following methods
would be most practical (and correct) for you to use? (2)
a) z- test comparing two means
b) t- test comparing two means assuming equal variances
c) t- test comparing two means not assuming equal variances
d) t- test comparing two means for paired data
e) z- test comparing two proportions
f) None of the above . (Give the correct one!)
[17]
8.
Referring to Exhibit 2, assume that the correct alternate formula for a critical value is
d cv  D0  t  2 s d , where t can be replaced by z for one method. What is the value of sd ? (3)
[20]
9.
Referring to Exhibit 2, and the previous problems, what is the value of the test ratio that we would
use to test your hypothesis? (2)
10. Referring to Exhibit 2, and the previous problems, assuming that your null hypothesis is correct, do
you reject the null hypothesis? Why? (2)
[24]
11. (Extra credit) compute a two-sided confidence interval for the ratio of the two variances in the
previous problem. (3)
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252x0622 11/08/06
Exhibit 3
You drive a New York avenue with 25 traffic lights on it. You suspect that this is equivalent to playing a
game with a constant probability of success (There are 25 tries.) You record the number of red lights you
hit on 50 trips up the avenue and from the data you come to the conclusion that the (sample) probability of
success is .5. You use a binomial table  p  .5, n  25  to figure out the probabilities of getting various
numbers of red lights on a single run and then you record the number of times you get these numbers of red
lights during the 50 trips up the avenue.
The left column is copied from my cumulative binomial table. The next column comes from
differencing the first column. The third column is the second column multiplied by 50. The fourth column
gives the numbers actually observed. The last two columns show the process of making the observed data
into a cumulative distribution.
E
O
Cum O Cum O
n
5.7380
6
6
.120
Px  9  0.11476
Px  9  0.11476
Px  10   0.21218
Px  11  0.34502
Px  12   0.50000
Px  13   0.65498
Px  14   0.78782
Px  15   0.88524
Px  25   1.00000
Px  10   0.09742
Px  11  0.13284
Px  12   0.15498
Px  13  0.15498
Px  14   0.13284
Px  15   0.09742
Px  16   0.11476
4.8710
8
14
.280
6.6420
6
20
.400
7.7490
4
24
.480
7.7490
6
30
.600
6.6420
6
36
.720
4.8710
8
44
.880
5.7380
6
50
1.00
12. Referring to Exhibit 3. The correct way to test for the distribution cited is: (2)
a) Kolmogorov-Smirnoff Test
b) Lilliefors Test
c) Chi-squared test with 8 degrees of freedom
d) Chi-squared test with 7 degrees of freedom
e) Chi-squared test with 6 degrees of freedom
f) z test for a proportion
g) None of the above. (Give the correct one!)
[26]
.
13. Referring to Exhibit 3. Assume that your choice of method in the previous problem is correct.
Carry out the test. (4)
[30]
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252x0622 11/08/06
14. An exit poll of 613 voters in Hotzeplotz yields the following results.
Conservative Moderate Liberal Sum
Voted Democrat 100
156
143
399
Voted Republican 127
72
15
214
Sum
227
228
158
a) A political expert has stated that the electorate is equally divided among the three ideological groups.
What would our E column be if this is true? (1)
b) Put together an O column and do a chi-square test of the hypothesis that the political expert has
mentioned. (3)
c) Do a confidence interval for the difference between the proportion of Democrats that are conservatives
and the proportion of Republicans that are conservatives.
d) Make an 87% confidence interval for the same difference. Do not use the t table.
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15. (Abramovic) Two independent samples, one of ten randomly selected women and the second of
ten randomly selected men are shown below.
Female Male
1
467
514
2
470
512
3
470
470
4
465
409
5
466
507
6
461
505
7
460
502
8
459
501
9
449
495
10
446
497
If we wish to show that male results exceed female results and suspect that the underlying
distribution is not Normal. We should use: (2)
a) Sign Test
b) Wilcoxon-Mann-Whitney Test for independent samples
c) Wilcoxon signed rank test
d) t-test for paired data
e) t-test for independent samples with equal variances.
f) F-test.
g) None of the above. (Give the correct one!)
16. Turn in your computer output for the first problem only. To get full credit it must be noted what
hypotheses were tested and what were the results. Use a 5% significance level. (4)
[41]
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252x0622 11/08/06
ECO252 QBA2
SECOND EXAM
November 7-8
TAKE HOME SECTION
Name: _________________________
Student Number: _________________________
Class days and hour: _________________________
III. Do at least 3 problems (at least 7 each) (or do sections adding to at least 20 points - Anything extra you
do helps, and grades wrap around) . Note: Look at 252thngs (252thngs) on the syllabus supplement part of
the website before you start (and before you take exams). Show your work! State H 0 and H 1 where
appropriate. You have not done a hypothesis test unless you have stated your hypotheses, run the
numbers and stated your conclusion.. (Use a 95% confidence level unless another level is specified.)
Answers without reasons usually are not acceptable. Neatness and clarity of explanation are
expected. This must be turned in when you take the in-class exam. Note that from now on neatness
means paper neatly trimmed on the left side if it has been torn, multiple pages stapled and paper
written on only one side.
1.
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A bank is testing various ways to serve walk-in customers. It tries 10 different new ways to
organize this service and gets the following results. Each result can be considered as a random
sample of 14 times that it takes a teller to serve ten walk-in customers. The data is presented
below. Method 1 is the method currently in use. You are asked to compare method 1 with one
other method by comparing the mean or median time it takes to serve the customers and to find out
if there is a significant difference between the methods. On the basis of your results you can
conclude that i) the old method is better, ii) the new method is better or iii) more information is
needed to make a decision. The second method to compare to method 1 is determined by the
second to last digit of your student number: if it is 0 use method 10; if it is 1 use method 11. If it is
2, 3, 4 etc use the method with the corresponding number. Label this problem clearly with the
number of the method that you are comparing with Method 1.
Method
1
2.9
3.9
2.6
3.1
3.9
2.6
3.3
3.0
3.5
3.1
3.2
2.4
4.0
4.3
2
2.8
2.6
2.6
2.9
2.9
2.8
2.3
2.4
2.0
2.5
2.4
2.0
4.1
4.3
3
2.6
2.7
3.2
2.8
3.6
2.1
2.3
2.6
2.6
2.9
2.4
2.3
0.5
4.7
4
7.7
2.9
4.3
2.7
3.4
4.4
5.5
3.4
3.4
3.5
4.0
3.4
4.1
3.8
5
2.4
13.4
5.8
1.5
9.8
2.7
2.7
4.5
2.3
5.8
4.8
4.2
5.8
6.1
6
6.6
3.7
9.7
1.9
10.1
4.5
2.9
9.9
3.0
31.5
3.5
5.3
9.8
5.3
7
3.5
8.4
4.3
3.3
11.9
3.7
3.0
2.9
3.6
5.4
4.4
3.0
4.3
5.4
8
3.4
8.3
4.2
3.2
11.0
3.6
2.9
2.8
3.5
5.3
4.3
2.9
4.2
5.3
9
3.5
3.4
3.8
3.4
3.6
3.5
4.8
3.5
5.3
3.7
3.4
3.6
3.8
3.8
10
2.3
6.9
3.3
5.3
3.0
3.3
6.1
3.1
2.6
4.4
15.0
6.9
2.1
10.4
11
3.4
4.4
3.1
3.6
4.4
3.1
3.8
3.5
4.0
3.6
3.7
2.9
4.5
4.8
Minitab gives us the following computations for Method 1. n  14, x  3.271, s x  0.155,
s  0.580, Minimum  2.400 Q1  2.825, x.50  3.150, Q3  3.900, Maximum  4.300. For
other information, see the end of this document. You can assume that the data for method 1 has an underlying Normal
distribution. Use a 95% confidence level.
a) Compute a standard deviation for the method that you are comparing with Method 1. Carry at
least as many significant figures as you see in the Minitab computations above. (1)
b) Test for a significant difference between the methods on the assumption that your method
represents data taken from the Normal distribution and the times have approximately equal variances. Use a
test ratio, critical value or a confidence interval (3) or all three (6).
c) Assume that the data represents a Normally distributed population but the variances are not
equal (4 – extra credit)
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252x0622 11/08/06
d) Assume that the Normal distribution does not apply. (4)
e) Test to see if the data from your method is Normally distributed (3)
f) Test to see if the standard deviations of the two methods are equal (1)
g) On the basis of the sections of this problem that you have been able to do write a
recommendation. (1)
[11]
[16]
2.
A researcher asked a group of artists and non- artists whether they believed in extra-sensory
perception. The data assembled is as below.
Of 114 artists, 58.77% believed in extrasensory perception. 35.96% more or less
believed in extrasensory perception and the remainder did not believe.
Of 344 non artists, 37.50% believed in extrasensory perception, 53.20% more or less
believed and the remainder did not believe.
a) Is there any association between being an artist and believing in ESP? (6)
b) Do a confidence interval for the difference in proportions who do not believe in ESP among
artists and non artists. Is the difference significant? (2)
[24]
3.
A researcher wants to see if the type of vehicle driven affects safety related behavior. The
researcher observes the following behavior at a stop sign on a rural intersection.
Behavior
Sedan Wagon Van
SUV
Stopped
180
24
30
14
Rolled through 107
18
10
20
Ran sign
60
8
11
16
Personalize the data as follows: To the number 180, add the last digit of your student number.
a) Is there an association between the vehicle driven and behavior? (5)
b) Cut down the number of rows in the problem by adding together the people who stopped and
rolled through. Assume that you were testing the hypothesis that the proportion of individuals who
who ran the stop sign was independent of the type of vehicle driven and that you had rejected your
null hypothesis. Use a Marascuilo procedure to find the 6 possible differences between
proportions and to find out if there are any pairs of vehicle types where the difference between the
proportions is insignificant. (4)
[33]
There will be extra credit offered for verifying your results using Minitab. A chi squared test can
be done by putting columns of data in without any totals and following the procedure used in the first part
of 252chisqx2. To compare two columns you can use the following instructions.
MTB >
SUBC>
MTB >
SUBC>
MTB >
MTB >
SUBC>
MTB >
SUBC>
normtest c2;
kstest.
VarTest c1 c2;
Unstacked.
TwoSample c1 c2.
TwoSample c1 c2;
Pooled.
Mann-Whitney 95.0 c1
Alternative 0.
#To test for normality.
#To test for equal variances.
#To compare means
#To compare means with equal variances assumed.
c2;
#To compare medians.
You will not be familiar with all the procedures used, but to get credit, you should be able to say in a
general way what was tested and what the results were.
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252x0622 11/08/06
Additional computations for the material in Problem 1. The data for methods 2-11 were stacked with
method 1 as shown below.
Method
Row 2
3
4
5
6
7
8
9
10
11
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
2.9
3.9
2.6
3.1
3.9
2.6
3.3
3.0
3.5
3.1
3.2
2.4
4.0
4.3
2.8
2.6
2.6
2.9
2.9
2.8
2.3
2.4
2.0
2.5
2.4
2.0
4.1
4.3
2.9
3.9
2.6
3.1
3.9
2.6
3.3
3.0
3.5
3.1
3.2
2.4
4.0
4.3
2.6
2.7
3.2
2.8
3.6
2.1
2.3
2.6
2.6
2.9
2.4
2.3
0.5
4.7
2.9
3.9
2.6
3.1
3.9
2.6
3.3
3.0
3.5
3.1
3.2
2.4
4.0
4.3
7.7
2.9
4.3
2.7
3.4
4.4
5.5
3.4
3.4
3.5
4.0
3.4
4.1
3.8
2.9
3.9
2.6
3.1
3.9
2.6
3.3
3.0
3.5
3.1
3.2
2.4
4.0
4.3
2.4
13.4
5.8
1.5
9.8
2.7
2.7
4.5
2.3
5.8
4.8
4.2
5.8
6.1
2.9
3.9
2.6
3.1
3.9
2.6
3.3
3.0
3.5
3.1
3.2
2.4
4.0
4.3
6.6
3.7
9.7
1.9
10.1
4.5
2.9
9.9
3.0
31.5
3.5
5.3
9.8
5.3
2.9
3.9
2.6
3.1
3.9
2.6
3.3
3.0
3.5
3.1
3.2
2.4
4.0
4.3
3.5
8.4
4.3
3.3
11.9
3.7
3.0
2.9
3.6
5.4
4.4
3.0
4.3
5.4
2.9
3.9
2.6
3.1
3.9
2.6
3.3
3.0
3.5
3.1
3.2
2.4
4.0
4.3
3.4
8.3
4.2
3.2
11.0
3.6
2.9
2.8
3.5
5.3
4.3
2.9
4.2
5.3
2.9
3.9
2.6
3.1
3.9
2.6
3.3
3.0
3.5
3.1
3.2
2.4
4.0
4.3
3.5
3.4
3.8
3.4
3.6
3.5
4.8
3.5
5.3
3.7
3.4
3.6
3.8
3.8
2.9
3.9
2.6
3.1
3.9
2.6
3.3
3.0
3.5
3.1
3.2
2.4
4.0
4.3
2.3
6.9
3.3
5.3
3.0
3.3
6.1
3.1
2.6
4.4
15.0
6.9
2.1
10.4
The numbers in each column above were ranked as follows.
Method
Row 2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
15.0
23.5
9.5
18.5
23.5
9.5
21.0
17.0
22.0
18.5
20.0
5.0
25.0
27.5
12.5
9.5
9.5
15.0
15.0
12.5
3.0
5.0
1.5
7.0
5.0
1.5
26.0
27.5
14.5
24.5
9.0
17.5
24.5
9.0
21.0
16.0
22.0
17.5
19.5
5.5
26.0
27.0
9.0
12.0
19.5
13.0
23.0
2.0
3.5
9.0
9.0
14.5
5.5
3.5
1.0
28.0
5.5
19.5
2.5
8.5
19.5
2.5
11.0
7.0
16.5
8.5
10.0
1.0
21.5
24.5
28.0
5.5
24.5
4.0
13.5
26.0
27.0
13.5
13.5
16.5
21.5
13.5
23.0
18.0
9.0
16.5
5.5
11.5
16.5
5.5
14.0
10.0
15.0
11.5
13.0
3.5
18.0
20.0
3.5
28.0
24.0
1.0
27.0
7.5
7.5
21.0
2.0
24.0
22.0
19.0
24.0
26.0
5.5
16.5
3.5
9.5
16.5
3.5
12.0
7.5
13.5
9.5
11.0
2.0
18.0
19.0
23.0
15.0
24.0
1.0
27.0
20.0
5.5
26.0
7.5
28.0
13.5
21.5
25.0
21.5
4.5
18.5
2.5
9.5
18.5
2.5
12.5
7.0
14.5
9.5
11.0
1.0
20.0
22.0
14.5
27.0
22.0
12.5
28.0
17.0
7.0
4.5
16.0
25.5
24.0
7.0
22.0
25.5
6.0
18.5
2.5
9.5
18.5
2.5
13.0
8.0
15.5
9.5
11.5
1.0
20.0
23.5
14.0
27.0
21.5
11.5
28.0
17.0
6.0
4.0
15.5
25.5
23.5
6.0
21.5
25.5
4.0
23.5
2.5
6.5
23.5
2.5
9.0
5.0
14.5
6.5
8.0
1.0
25.0
26.0
14.5
11.0
21.0
11.0
17.5
14.5
27.0
14.5
28.0
19.0
11.0
17.5
21.0
21.0
2.9
3.9
2.6
3.1
3.9
2.6
3.3
3.0
3.5
3.1
3.2
2.4
4.0
4.3
3.4
4.4
3.1
3.6
4.4
3.1
3.8
3.5
4.0
3.6
3.7
2.9
4.5
4.8
10
7.0
18.5
5.0
11.0
18.5
5.0
15.0
8.5
17.0
11.0
13.0
3.0
20.0
21.0
2.0
25.5
15.0
23.0
8.5
15.0
24.0
11.0
5.0
22.0
28.0
25.5
1.0
27.0
11
4.5
20.5
2.5
8.5
20.5
2.5
12.0
6.0
14.5
8.5
11.0
1.0
22.5
24.0
13.0
25.5
8.5
16.5
25.5
8.5
19.0
14.5
22.5
16.5
18.0
4.5
27.0
28.0
10