# Use the information given in the paragraph below to answer the

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COURSE: MSCI 3710                          PRINT Name:

Exam 1                                     Signature:

Version B                                  Student ID#:

Spring 2002                                Seat Number:

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Also, put your signature on this exam.

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      You have 75 minutes to complete this exam. The exam is open book, open
notes, and open mind. You may use any type of calculator, but please show
all your work on the exam and mark all answers on the scantron.

Statistics. The remaining questions are either based on Excel outputs, or use
an Adventures-like approach with problems similar to those assigned in the
textbook. The chapter numbers given against in questions are only
indicative, and you may need to integrate the concepts from other chapters.

      Do not detach this exam. When you have completed the exam, please insert
the scantron into the exam booklet and return them both to your instructor.

      No cheating.

      Good luck and we wish you well on the exam.

Note: Whenever question(s) are connected you may be asked to assume
a result (i.e., given a value as answer to a previous question); but this
result (i.e., the given value) need not be the correct response for the
previous question. This is done only to prevent you from losing points
on a subsequent question because you made a mistake on one.
Use the paragraph below to answer the next six questions (Kvanli Chapter 8).

The Caribbean boasts of inexpensive weddings. From past data, the average cost of a
wedding is known to be \$7400, with a standard deviation of \$1050. To test if the true
mean costs have changed, a random sample of 30 current weddings is taken. Their
average is \$7720. Is there evidence that currently, the true mean cost of wedding differs
from the usual \$7400? Perform the test at = 0.05.

1. What are the null hypothesis and alternative hypothesis for this test?
A. Ho:  = 7720 Ha:  7720
B. Ho:   7720 Ha:  < 7720
C. Ho:  = 7400 Ha:  
D. Ho:  > 7400 Ha:  
E. Ho:  = 7400 Ha:  <7400

2. The appropriate test statistic for testing the hypothesis as defined in question #1 is
A. t because the sample size is small
B. t because the sample standard deviation was calculated
C. Z because the population standard deviation is known *
D. Z because the sample variance was provided
E. F because we do not know the equality of the variance

3. What is the calculated value of the test statistic?
A. - 0.45
B. 1.67 *
C. 1.96
D. - 167
E. 1.645

4.Assuming the calculated value of the test statistic is 1.70, what are the decision and
conclusion of the test? (use  = 0.05)
A. Fail to reject the null hypothesis, conclude there is insufficient evidence the
average wedding cost is not equal to \$7400. *
B. Fail to reject the null hypothesis, conclude there is overwhelming evidence the
average wedding cost is equal to \$7400.
C. Fail to reject the null hypothesis, conclude there is evidence the average wedding
cost is not equal to \$7400.
D. Reject the null hypothesis, conclude there is evidence the average wedding cost is
not equal to \$7400.
E. Reject the null hypothesis, conclude there is insufficient evidence the average
wedding cost is not equal to \$7400.

5. At the 0.05 level of significance, where is the Reject Ho region?
A. To the left of Z = - 2.33 and to the right of Z = 2.33
B. To the left of Z = -1.645 and to the right of Z = 1.645
C. Between Z = -1.645 and Z = 1.645
D. To the left of Z = -1.96 and to the right of Z = 1.96 *
E. Between Z = -1.96 and Z = 1.96

6. If the computed value of the test statistic is 1.96, what is the p-value?
A. 0.10       B. 0.05*                 C. 0.025         D. 0.01        E. 0.005

Use the information given in the following paragraph to answer the next four
questions (Kvanli Chapter 8).
The manager at the Sun and Sea Hotel believes the average expenditure per night for
guests sharing the same room is greater than \$195. A random sample of 20 rooms was
selected and the expenditure by the guests was recorded. The Excel results are shown
below:

t Test for Population Mean
Expend
Number of Observations              20
Sample Standard Deviation        35.226837
Sample Mean                 210.657500

T*                     XXXXX
P[T  T*]                  XXXXX
T Critical, =0.05            1.729131
95% CI for Pop. Mean           194.170828     to   227.144172

7. What is the alternative hypothesis for this test?
A. Ha:  > 210
B. Ha:  210
C. Ha:  < 195
D. Ha:  > 195 *
E. Ha:  < 200

8.What is the calculated test statistic to test the manager’s belief?
A. - 1.83
B. 1.99 *
C. 0.17
D. 1.05
E. - 2.02

9. Suppose the calculated test statistic is 1.85. Which one of the following would best
describe the p-value of the test?
A.      p > .1
B.      .05 < p < .10
C.      .025 < p < .05 *
D.      .01 < p < .025
E.      p < .01
10. Suppose the p-value of the test is 0.03. What is the conclusion of the test concerning
the potential buyer’s belief, conducted at the 0.01 significance level, and reason for
the conclusion?
A. Conclude there is insufficient evidence the average room costs is greater than \$195
because the p-value is greater than the significance level. *
B. Conclude there is evidence the average room costs is greater than \$195 because the p-
value is greater than the significance level.
C. Conclude there is evidence the average room costs is greater than \$195 because the p-
value is smaller than the significance level.
D. Conclude there is insufficient evidence the average room costs is greater than \$195
because the p-value is smaller than the significance level.
E. Conclude there is evidence the average room costs is at least \$195 because the test
statistic is greater than the significance level.

Information given in the paragraph below to answer the next four questions. (Kvanli
Chapter 9)

What’s in a name? Do companies with cyber, link or web (the “tech”-words) in their
name have a different growth rate than those who don’t? To test this idea random
samples of companies with or without these words in their names were selected and their
percentage growth was recorded. The results are recorded below:

Growth with “tech” words (1)           Growth without “tech” words (2)
x      27.5                                   23.6
s       4.5                                    3.4
n       15                                     13

11.Assuming the variance in the growth rate of the companies with the “tech” words is
equal to that for the companies without the “tech” words, what is the pooled variance?
A. 19.2
B. 16.2 *
C. 11.0
D. 12.0
E. 25.0

12. Assuming the variance in the growth rate of the companies with the “tech” words is
equal to that for the companies without the “tech” words, what is the critical value of the
test statistic (absolute value) for testing whether the growth rates are any different? (use 
= 0.05)
A. 2.326
B. 1.684
C. 2.056*
D. 2.423
E. 1.645
13.Assuming the pooled standard deviation was 4.45. What is the calculated value of the
test statistic for testing whether the growth rates are different?
A. 2.76
B. - 5.49
C. 1.56
D. 2.31 *
E. - 3.55

14.Suppose the absolute value of the calculated test statistic is 2.65. Which one of the
following would best describe the p-value of the test?
A. p > .1
B. .05 < p < .10
C. .025 < p < .05
D. .01 < p < .02*
E. p < .01

Use the information given in the following paragraph to answer the next five
questions. (Kvanli Chapter 10)

The vice president of Dorite Energy company believes that less than 70% of the
shareholders of the company read the annual report. From a random sample of 190
shareholders, 124 read the annual report. Test the vice president’s belief. Use a .01
significance level.

15. What are the hypotheses for this test?
A.   Ho: p = 0 Ha: p  0
B.   Ho: p < .80 Ha: p > .80
C.   Ho: p > .70 Ha: p < .70 *
D.   Ho: p < .65 Ha: p > .65
E.   Ho: p > .65 Ha: p < .65

16. What is the necessary sample size to estimate p within .08 with 99% confidence? Use
the results of the sample of 190 shareholders.
A. 204
B. 135
C. 166
D. 658
E. 237*

17. What is the value of the calculated test statistic?
A. -1.43 *
B. -2.88
C. -2.38
D. 1.68
E. -3.68

18. Construct a 99% confidence interval for estimating the proportions of shareholders of
the company that read the annual report.
A.   0 to 0.053
B.   -0.018 to 0.087
C.   -0.036 to 0.053
D.   0.563 to 0.742 *
E.   0.009 to 0.063

19. The test procedure using a 1% level of significance is to reject Ho if the calculated
test statistic is

A.   < -2.33 or > 2.33
B.   < -2.33*
C.   < -1.96 or > 1.96
D.   > 2.33
E.   < 1.645

Use the following information to answer the next six questions. (Kvanli Chapter 11)

Custom Flooring is testing three types of adhesives for laying linoleum. Each glue is
tested on five different surfaces if there is any difference between the adhesives. The
adhesiveness of the glue is measured, and the coded results are shown below. The
partially filled ANOVA Table below shows the results of the analysis of the data (at the α
= .05 level) in which they employed a randomized block design with surface as the
blocking variable.
1        5.4         5.1        5.1
2          5         4.5          4
3        4.5         3.4        3.5
4        3.5         2.9        2.8
5        3.6           3        3.5
Anova: Two-Factor Without Replication

SUMMARY                    Count   Sum Average Variance
1       3    15.6    5.2     0.03
2       3    13.5    4.5     0.25
3       3    11.4    3.8     0.37
4       3     9.2  3.07      0.14
5       3    10.1  3.37      0.10

Adhesive 1                                    5   22     4.4    0.705
Adhesive 2                                    5 18.9    3.78    0.947
Adhesive 3                                    5 18.9    3.78    0.727

ANOVA
Source of Variation          SS     df      MS       F       P-value      F crit
Rows (Surface)                      XXX     4     2.251     XXXX         XXXX      XXXX
Columns (Adhesive)                  XXX     2     0.641     XXXX         XXXX      XXXX
Error                               0.51    8     0.064

Total                                10.8 14

20. What is the calculated value for testing the claim that there is a difference between
A. 10.02*
B. 9.34
C. 7.56
D. 1.37
E. 4.46

21. Which of the following would be the appropriate alternative hypothesis for testing
the claim that the effect of the ‘adhesive’ is significant?
A. Ha: μ1 = μ2 = μ3
B. Ha: μ1  μ2  μ3
C. Ha: μ1 = μ2 < μ3
D. Ha: μ1  μ2 < μ3
E. Ha: At least one pair of μ1, μ2, μ3 is different *

22. What are decision and conclusion for testing the effect of the adhesive assuming the
calculated value of the test statistic is 7.0 (at α = .05)?

A. Reject the null hypothesis since the test statistic is relatively large. The means of
effect of the adhesives are all the same.
B. Reject the null hypothesis since the test statistic is relatively large. The means of
effect of the adhesives are not all the same. *
C. F.T.R. the null hypothesis since the test statistic is relatively large. The means
effect of the adhesives are all the same.
D. F.T.R. the null hypothesis since the test statistic is relatively small. The means
effect of the adhesives are all the same.
E. F.T.R. the null hypothesis since the test statistic is relatively small. The means
effect of the adhesives are not all the same.

23. How much variation is due to the different surfaces?
F.    6.55
G.    9.00 *
C.    16.50
D.    11.07
E.    52.29

24. What is the calculated value of the statistic for testing that the effect of the surfaces is
significant?
A.      35.17*
B.      0.91
C.      7.564
D.      15.33
E.      21.46

25. Suppose the calculated test statistic for the effect of the surfaces is 6.50. Which one
of the following would best describe the p-value of the test?
A. p > .1
B. .05 < p < .10
C. .025 < p < .05
D. .01 < p < .025 *
E. p < .01

Thank you!

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