COURSE: DSCI 3710
Exam 1
5W2 2013
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Note: Whenever question(s) are connected you may be asked to assume a result (given
a value) as an answer for the previous question but this result (value) may or may not
be correct. The procedure is set in place to prevent you from losing points on a
subsequent question because you made a mistake on some previous question/s.
Use the following paragraph for the next six questions.
The market researchers at Jenn’s restaurant are interested in the proportion of male customers
and female customers that would be willing to try a new salad. Random samples of 189 males
and 138 females were randomly selected. Responses were recorded as Yes (i.e. interested) or No
(i.e. not interested) and are listed as variables MalesInterested (1) and FemalesInterested (2). The
samples indicated that 73 males and 92 females respectively were interested in trying a new
salad. Test that the proportion of male customers interested is less than the proportion of female
customers interested. Use a significance level of α= 0.05 for the test. The KPK Macro output is
shown below.
Z Test for Two Proportions
Sample Proportion
Number of Observations
Ho:XXXX
Z*
P[Z  Z*]
Z Critical,  = 0.05
Variable 1
Variable 2
0.386
189
Ha:XXXX
-5.009
0.000
XXXX
0.666
138
1. What is the null hypothesis for the test?
A. Ho: p1 > p2
B. Ho : p1 ≠ p2
C. Ho : p1 ≥ p2
D. Ho : p1 < p2
E. Ho : p1 = p2
2. What is the point estimate of the proportion of females interested in trying a new salad?
A. 0.386
B. 0.482
C. 0.289
D. 0.666
E. 0.025
3. What is the critical (table) value of the test statistic?
A. 1.645
B. 1.96
C. -1.645
D. 2.33
E. -1.96
4. What is the calculated value of the test statistic?
A. -1.645
B. 2.33
C. -1.96
D. -5.009
E. -4.781
5. What is the estimated pooled proportion for males and females?
A. 0.0509
B. 0.0424
C. 0.0387
D. 0.5046
E. 0.9513
6. Assuming that the p-value were 0.024 what is the appropriate statistical decision for this
test?
A. Reject the Ho because the p-value is greater than the calculated test statistic.
B. Fail to reject the Ho because the p-value is greater than the calculated test statistic.
C. Reject the Ho because the p-value is smaller than the level of significance.
D. Fail to reject the Ho because the p-value is smaller than the level of significance.
E. Reject the Ho because the p-value is smaller than the critical (table) value of the test
statistic.
Use the information given in the next paragraph to answer the next question.
An accountant of Wallie’s the pizza franchise claims that its stores generate average weekly
revenues of at least $7,000 per store. A potential buyer who is considering purchasing a Wallie’s
pizza franchise is doubtful about this claim, and believes instead that the average weekly revenue
might be less than $7,000. With some effort, he obtains revenues from 20 Wallie’s stores across
the country by interviewing their managers/employees and finds that the average revenue is
$6400. Historical tax filings by Wallie’s indicate that the standard deviation of revenues has been
about $1042. Store revenues are assumed to be normally distributed.
7. What is the calculated value of the statistic to test the potential buyer’s belief at the 1%
level of significance?
A. 1.38
B. -2.58
C. 1.645
D. -2.33
E. -2.05
Use the information given in the next paragraph to answer the next two questions.
An accountant for Carry’s hamburger franchises claims that stores generate average monthly
revenue of $70,000 per store. She obtains a sample of revenues from 20 stores and conducts a
statistical analysis on the data using Excel, the results of which are shown below at 0.05
significance level.
t Test for Population Mean
Carry's
Number of Observations
Sample Standard Deviation
Sample Mean
Ho:XXXXX
T*
2 * P[T T*] two tail
| T Critical |,  = 0.05
95% CI for Pop. Mean
20
1213.376
73473.200
Ha:XXXXX
XXXXX
XXXXX
2.093
72905.322
to
74041.077
8. Which of the following would be appropriate for the alternative hypothesis?
A. Ha: μ = 70,000
B. Ha: μ ≤ 70,000
C. Ha: μ ≠ 70,000
D. Ha: μ < 70,000
E. Ha: μ > 70,000
9. Based upon the output shown above, what is the conclusion of the hypothesis test?
A. Conclude there is evidence the average monthly revenue is greater than $70,000
because the p-value is greater than the significance level.
B. Conclude there is evidence the average monthly revenue is not equal to $70,000
because the p-value is smaller than the significance level.
C. Conclude there is insufficient evidence the average monthly revenue is greater than
$70,000 because the p-value is greater than the significance level.
D. Conclude there is insufficient evidence the average monthly revenue is greater than
$70,000 because the p-value is smaller than the significance level.
E. Conclude there is evidence the average monthly revenue is at least $70,000 because
the test statistic is greater than the significance level.
Use the information given in the next paragraph to answer the next four questions.
Corporations have started paying attention to their employee fitness, with the spiraling costs of
their health insurance. Weight-loss for gains is a program aimed at their self-confessed obese
employees. The table below shows the weight (in pounds) of 10 such employees who
participated in a corporate physical training program that lasted 60 days. The weights shown are
those before and after completing the program, for each employee. Excel analysis at the 5%
significance level is also shown.
ID #
Employee 1
Employee 2
Employee 3
Employee 4
Employee 5
Employee 6
Employee 7
Employee 8
Employee 9
Employee 10
before
285
267
240
210
207
234
211
223
255
266
after
299
200
218
199
200
230
177
246
256
217
t-Test: Paired Two Sample for Means
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
239.8
224.2
756.622 1248.844
10
10
0.631
10
9
0.6346
0.271
1.833
0.541
2.262
10. What would be the table (critical) value (at the 5 % level) of the appropriate test statistic
to test the belief that there is a reduction of over 10 pounds in the mean weight if
employees go through the program?
A. 1.83
B. 2.26
C. 1.73
D. 2.10
E. 4.15
11. What is the calculated value of the appropriate test statistic to test the belief that there is a
reduction of over 10 pounds in the mean weight?
A. 0.1872
B. 0.4278
C. 0.6346
D. 0.8331
E. 0.4586
12. What is the p-value for testing the hypothesis that there is a reduction of over 10 pounds
in the mean weight of employees choosing to be in the program?
A. 0.1872
B. 0.2707
C. 0.8557
D. 0.8331
E. 0.4586
13. What is the point estimate based on the sample, for the mean weight loss for employees
taking part in the program?
A. 13.4
B. 10.2
C. 15.6
D. 26.8
E. 40.5
Use the information given in the next paragraph to answer the next four questions.
A cellular company operates three branch offices in the same city. To test for differences in the
effectiveness of the sales personnel at the different branches, independent samples of the average
dollar amounts of sales (in thousands) for personnel are taken and analysis using Excel was
completed. It is desired to test whether the dollar amount of sales differ for the branches at 5
percent level of significance.
Branch A
31
30
34
44
45
46
49
Branch B
33
39
66
42
48
62
55
Branch C
79
78
72
66
63
75
65
Anova: Single Factor
SUMMARY
Groups
Count
Sum Average Variance
Branch A
Branch B
7
7
279
345
39.857
49.286
62.476
149.905
Branch C
7
498
71.143
42.476
ANOVA
Source of Variation
SS
df
MS
Between Groups
Within Groups
3606
1529.143
2 XXXXXX
18 XXXXXX
Total
5135.143
20
F
P-value
F crit
XXXXXX
XXXXXXX 3.555
14. The correct alternative hypothesis to test whether the dollar amount of sales differs is:
A. Ha: All the means are equal.
B. Ha: All the means are different.
C. Ha: Not all means are equal.
D. Ha: At least two means are equal.
E. Ho: Not all means are equal.
15. The calculated value of the test statistic for the test in the above question is:
A. 30.98
B. 21.22
C. 19.43
D. 18.22
E. 19.11
16. From the above ANOVA, the company’s management should conclude that:
A. It is possible that all the branches have the same sales.
B. Not all the branches have the same sales.
C. Some branches have the same sales.
D. All branches have different sales.
E. Cannot be determined, need more information
17. Assuming the calculated test statistic were 30, what is the p-value?
A. Over 0.100
B. Between 0.050 and 0.100
C. Between 0.025 and 0.050
D. Between 0.010 and 0.025
E. Less than 0.010
Use the information given in the paragraph below to answer the next three questions.
The mayor of Smallville believes that less than 40% of its residents favor annexation of the Lake
Duchess community. A sample of 60 random residents of Smallville showed that 37% of the
residents favored annexation. Is there sufficient evidence at the 0.05 level to support the mayor's
claim?
18. What is the alternative hypothesis for this test?
A. Ha: p ≠ 0.37
B. Ha: μ > 0.37
C. Ha: μ ≠ 0.4
D. Ha: p > 0.4
E. Ha: p < 0.4
19. The decision rule, based on the critical value and 5% significance level, is Reject Ho if
the calculated value is,
A. < -1.96
B. >1.28
C. < -1.645
D. > 1.96
E. > 2.32
20. What is the observed level of significance (p-value) if the calculated test statistic is -1.86?
A. 0.9802
B. 0.0099
C. 0.4901
D. 0.0314
E. 0.9500
Use the information given in the next paragraph to answer the next five questions.
The personnel manager of Shark Inc. wishes to determine if the number of sick days reported by
each employee in 2008 at its Houston (H) plant was any different from the number of sick days
reported in 2008 at its San Antonio (S) plant. Random samples of employees in Houston (H) and
San Antonio (S) are selected, and the following results are obtained with Excel assuming equal
variances and significance level of 5 percent.
Houston (H)
9.5
12.3
5.5
7
9.5
14
6.1
9.3
4
6.4
San Antonio (S)
6.7
7.3
10
6.4
9.2
5.8
8.5
8
6.5
6
t-Test: Two-Sample Assuming Equal Variances
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
Houston (H)
8.36
9.867
10.000
5.955
0
18
0.843
XXXXXX
1.734
XXXXXX
2.101
San Antonio(S)
7.44
2.043
10
21. What is the alternative hypothesis for testing the difference of number of sick days?
A. Ha: μH – μS ≤ 15
B. Ha : μH – μS > 15
C. Ha : μH – μS < 0
D. Ha : μH – μS ≠ 0
E. Ha : μH – μS = 0
22. What is the critical value of the test statistic?
A. 2.101
B. 1.734
C. 0.9449
D. 0.9921
E. 0.1111
23. Assuming the variance in the number of sick days reported for all employees at the
Houston plant is equal to that for all employees at the San Antonio plant, what is the
calculated value of the test statistic for testing whether there is a difference in the number
of sick days reported?
A. 0.0101
B. 1.734
C. 0.843
D. 0.9921
E. 0.1111
24. What are the decision and conclusion of the test of hypothesis?
A. Reject Ha and conclude that the number of sick days reported in 2008 at Shark’s San
Antonio plant was different from that at its Houston plant.
B. Reject Ho and conclude that the number of sick days reported in 2008 at Shark’s San
Antonio plant was different from that at its Houston plant.
C. Reject Ho and conclude that the number of sick days reported in 2008 at Shark’s San
Antonio plant was not different from that at its Houston plant.
D. Fail to reject Ho and conclude that the number of sick days reported in 2008 at
Shark’s San Antonio plant was different from that at its Houston plant.
E. Fail to reject Ho and conclude that the number of sick days reported in 2008 at
Shark’s San Antonio plant was not different from that at its Houston plant.
25. Which one of the following would best describe the p-value of the test?
A. p > 0.200
B. 0.100 < p ≤ 0.200
C. 0.050 < p ≤ 0.100
D. 0.025 < p ≤ 0.050
E. p < 0.025
Use the following paragraph for the next three questions.
A manufacturer claims that the calling range (in miles) of its 900-MHz cordless telephone is
greater than its leading competitor. You perform a study using 14 phones from a manufacturer
and 16 similar phones from its competitor. The results are shown in the table. Assume that the
populations are normally distributed and the population variances are equal.
manufacturer
mean
standard deviation
sample size
Competitor
1119.286 mean
25.784 standard deviation
14 sample size
1114.063
20.994
16
26. What is the pooled variance?
A. 365.963
B. 676.074
C. 372.715
D. 554.779
E. 371.542
27. What are the degrees of freedom to test the appropriate hypothesis?
A. 20
B. 22
C. 24
D. 26
E. 28
28. What is the critical (table) value to test the null hypothesis at a significance level of 5%?
A. 1.313
B. 1.701
C. 2.048
D. 1.699
E. 1.697
Use the following paragraph for the next two questions
The CEO of Mean Green Trucking Company (MGT) is trying to decide which of three makes of
automobile to order for its fleet – Brand A, Brand B, or Brand C. Six trucks of each brand were
randomly ordered, and after 10,000 miles of driving, the operational cost per mile of each was
assessed. The accompanying results in cents per mile were obtained. Using a 5% significance
level an Analysis of Variance (ANOVA) was conducted on the data.
Brand
A
26
28
25
29
27
27
Brand
B
30
29
32
31
32
32
Brand
C
27
25
28
24
26
26
Anova: Single Factor
SUMMARY
Groups
Brand A
Brand B
Brand C
Count
6
6
6
Sum
162.000
186.000
156.000
Average
27.000
31.000
26.000
Variance
2.000
1.600
2.000
ANOVA
Source of
Variation
Between Groups
Within Groups
SS
84.00
28.00
df
2
15
MS
42.000
1.866
F
22.500
Total
112.00
17
TUKEY MULTIPLE
COMPARISON TEST
Critical Q
Distance
3.67
2.047
Alpha
0.05
Means joined by a double line are not significantly
different.
Brand C
26.000
Brand A
27.000
Brand B
31.000
P-value
0.00003
F crit
3.682
29. What is the Tukey’s critical distance?
A. 3.67
B. 3.187
C. 1.976
D. 1.838
E. 2.047
30. Suppose the CEO wants to choose a single automobile brand so as to minimize MGT’s
operational cost. Which brand should he choose?
A. Brand A
B. Brand B
C. Brand C
D. Brand A or C
E. There is insufficient information given to decide
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