Download 3710 Spring 2010 FinalA

COURSE: DSCI 3710
Print Name:
Exam 1 – version A
Signature:
Spring 2010
Student ID#:
INSTRUCTIONS:

Please print your name and student ID number on this exam. Also, put your
signature on this exam.

On your scantron PRINT your name and exam version. To better protect your
privacy also print your name on the backside of your scantron.

You have 105 minutes to complete this exam. The exam is open book, open
notes, and open mind. You may use any type of hand calculator but please show
all your work on the exam and mark all answers on the scantron. Usage of cell
phones, digital cameras, PDAs, and other communication devices is strictly
prohibited.

Many of the questions follow the format of those in Hawkes Learning Systems
Business Statistics. The remaining questions are either based on the Excel
assignments or use an HLSBS-like approach with problems nearly identical to
those assigned in the textbook.

Please DO NOT pull this exam apart. When you have completed the exam, please
turn in your scantron and exam booklet to your instructor, at the front desk.

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 (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 information given below to answer the 4 questions that follow:
A corporation randomly selects 150 salespeople and finds that 125 who have never taken a selfimprovement course that would like a course. The firm did a similar study 10 years ago in which
120 of a random sample of 160 salespeople wanted a self-improvement course. The groups are
assumed to be independent random samples. Let p1 and p2 represent the true proportion of
workers who would like to attend a self-improvement course in the current study and the past
study respectively. The firm wants to test whether their current course recruitment efforts
resulted in a greater proportion of workers that want to attend a self-improvement course than in
the past.
Z Test for Two Proportions
Sample Proportion
Number of Observations
Ho: XXX
Z*
P[Z  Z*]
Z Critical,  = 0.01
99% CI for p1 - p2
Variable 1
Variable 2
0.833333
150
Ha: XXX
1.801215
0.035835
X.XX
-0.035026
0.750000
160
to
0.201692
1. What are the correct null and alternative hypotheses for the above situation?
A. Ho: μ1 > μ2 Ha: μ1 < μ2
B. Ho: p1 < p2 Ha: p1 > p2*
C. Ho: p1 = p2 Ha: p1 ≠ p2
D. Ho: p1 > p2 Ha: p1 < p2
E. Ho: μ1 = μ2 Ha: μ1 ≠ μ2
2. What is the critical value for testing the hypotheses for this problem if  = 0.01?
A. 1. 645
B. 1.96
C. 2.33*
D. 2.57
E. 1.28
3. What is the calculated value of the test statistic for the above statistical test?
A. -0.09
B. 0.18
C. 0.16
D. 1.80*
E. 0.72
4. What are the decision and conclusion of the test at the significance level of 0.01?
A. Fail to reject the null hypothesis, conclude there is sufficient evidence that the proportion
of workers that want to attend the course has decreased.
B. Reject the null hypothesis, conclude there is no evidence of difference in proportions.
C. Fail to reject the null hypothesis, conclude there is insufficient evidence that the
proportion of workers that want to attend the course has increased.*
D. Reject the null hypothesis, conclude there is evidence that the proportion of workers that
want to attend the course has increased.
E. Fail to reject the null hypothesis, conclude there is sufficient evidence of difference in
proportions.
Use the information given below to answer the four (4) questions that follow:
The Glen Valley Steel Company manufactures steel bars. If the production process is working
properly, it turns out steel bars with an average length of at least 2.75 feet with a standard
deviation of 0.20 foot (as determined from engineering specifications on the production
equipment involved). Longer steel bars can be used or altered, but shorter bars must be scrapped.
A sample of 25 bars is selected from the production line. The sample indicates an average length
of 3.08 feet. The company wishes to determine whether the process is making short bars because
if it is, then the production equipment needs an immediate adjustment.
t Test for Population Mean
Number of Observations
Sample Standard Deviation
Sample Mean
Ho: X.XX
T*
P[T  T*]
T Critical,  = 0.05
95% CI for Pop. Mean
25
0.606218
3.080000
Ha: < X.XX
2.721794
0.994052
-1.710882
2.829766
to
5. State the null and alternative hypothesis.
A. Ho: µ ≥ 2.75; Ha: µ < 2.75 *
B. Ho: µ < 2.75; Ha: µ ≥ 2.75
C. Ho: µ ≥ 2.75; Ha: µ ≠ 2.75
D. Ho: µ = 2.75; Ha: µ ≠ 2.75
E. Ho: µ ≥ 2.75; Ha: µ = 2.75
6. What is the degree of freedom?
A. 25
B. 24*
C. 26
D. 27
E. 28
7. At the 10% level of significance, where is the Reject Ho region?
A. To the left of T = -1.318 *
B. To the left of T = -1.645 and to the right of T = 1.645
C. To the left of Z = -1.328 and to the right of Z = 1.328
D. To the right of T = -1.711
E. To the left of T = -1.960
3.330234
8. Assuming the calculated value of the test statistic is -1.25, what are the decision and
conclusion of the test at the significance level of 0.05?
A. Fail to reject the null hypothesis; there is insufficient evidence to conclude that the process is
not making short bars.
B. Reject the null hypothesis, there is sufficient evidence to conclude that the process is not
making short bars.
C. Fail to reject the null hypothesis, there is insufficient evidence to conclude that the process is
making short bars.*
D. Reject the null hypothesis, there is insufficient evidence to conclude that the process is not
making short bars.
E. Reject the alternative hypothesis; conclude the mean is significantly less than 2.75 feet.
Use the information given below to answer the four questions that follow:
The effect of a corporate contract-training course on employee efficiency is the subject of a
study. Based on advice from a statistics consultant, the human resources training specialist
assigned two sets of 10 pages of equally difficult material for data entry by the same 10 staff
members, with one set being entered before and the other after completing the corporate
contract-training course. The raw data with the number of errors and Excel analysis using a
10% significance level are shown in the Tables below.
Typist
1
2
3
4
5
6
7
8
9
10
Before
31
30
35
43
36
34
.
.
43
45
After
30
33
36
38
30
28
.
.
40
47
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
35.6
43.1556
10
0.85156
0
9
1.07763
0.XXXX
1.38303
0.XXXX
1.83311
After
34.4
40.0444
10
9. What is the table value of the appropriate test statistic to test the belief at the 10% level of
significance that there is a reduction in the mean number of errors if data entry personnel go
through the contract-training course?
A. 1.38 *
B. 1.83
C. 1.08
D. 0.86
E. 2.03
10. What is the calculated value of the appropriate test statistic to test the belief that there is a
reduction in the mean number of errors if data entry personnel go through the training course?
A. 1.38
B. 1.08 *
C. 1.83
D. 0.86
E. 1.96
11. Which of the following ranges best represents the p-value (calculated t statistic) for testing
the belief that there is a reduction in the mean number of errors if data entry personnel go
through the contract-training course?
A. p > 0.1*
B. 0.05 < p < 0.1
C. 0.025 < p < 0.05
D. 0.01 < p < 0.025
E. p < 0.01
12. What are the decision and conclusion of the test?
A. Fail to reject the null hypothesis, conclude there is insufficient evidence for error reduction. *
B. Fail to reject the null hypothesis, conclude there is sufficient evidence for error reduction.
C. Reject the null hypothesis, conclude there is evidence for error reduction.
D. Reject the null hypothesis, conclude there is no evidence for error reduction.
E. No decision or conclusion can be reached from this analysis
Use the information in the paragraph below to answer the next five questions.
A grocery store wants to learn about the preferred shopping times for customers of different age
groups. A random sample of customers of the store was selected, and information was gathered
on their shopping time preference and age classification. A chi-square test of independence was
performed at the 0.05 significance level using Excel with the three age categories in the rows and
the three different time categories in the columns. A Chi –square test of independence using
Excel gave the following Tables.
Cross tabulation Table
OBSERVED
Coln 2
25
27
XX
73
Calculation of the Chi-Square Test
DESCRIPTION
VALUE
Row 1
Row 2
Row 3
Total
Coln 1
XX
XX
26
83
Coln 3
24
30
19
73
Total
78
85
66
229
Row 1
Row 2
Row 3
Total
EXPECTED
Coln 1 Coln 2 Coln 3
28.271 24.865 24.865
30.808 27.096
XXX
23.921
XXX
XXX
83
73
73
Total
78
85
66
229
2*
p-value
Critical value

df
0.995441
XXX
9.487729
0.05
4
13. What alternative hypothesis would you use to test whether there is a relationship between
age and preferred shopping time?
A. Ha: The means of the preferred shopping times are different.
B. Ha: The age range is independent of the preferred shopping time.
C. Ha: The preferred shopping time depends on the customers’ age range.*
D. Ha: Each of the three preferred shopping times is the same.
E. Ha: The three age ranges prefer a different mean shopping time.
14. What is the calculated value of the test statistic for this statistical test?
A.
0.05
B.
0.995*
C.
0.910
D.
9.487
E.
4
15.
A.
B.
C.
D.
E.
Based on the Excel output given above, what is the conclusion of the test of this hypothesis?
There is sufficient evidence that the means of the preferred shopping times are not equal.
There is sufficient evidence that age range and preferred shopping time are dependent.
There is sufficient evidence that the three age ranges prefer the same shopping time.
There is insufficient evidence that age range and preferred shopping time are dependent.*
There is insufficient evidence that the means of the preferred shopping times are not equal.
16. What is the degrees of freedom value for this chi-square test?
A. 9
B. 8
C. 6
D. 4 *
E. 2
17. Which of the following ranges best describes the p-value for the test statistic?
A. p > 0.05*
B. 0.025 < p-value < 0.05
C. 0.01 < p-value < 0.025
D. 0.001 < p-value < 0.01
E. p < 0.001
Use the following information to answer the next six questions.
A medical researcher was interested in the amount of weight loss caused by a particular diuretic.
In a controlled experiment with 20 mice, the amount of weight loss was recorded after 1 month
of fixed daily doses of the diuretic, administered as follows: (A partial output of the regression
analysis of the data are given subsequently.)
Rat
1
2
3
Diuretic
(milligrams)
Weight Loss
(pounds)
0.30
0.30
0.35
0.35
0.38
0.41
11
12
0.45
0.50
0.50
0.61
0.71
0.72
18
Rat
13
Diuretic
(milligrams)
Weight Loss
(pounds)
0.55
0.55
0.60
0.73
0.72
0.74
0.70
0.55
0.55
0.83
0.49
0.51
.
.
.
.
8
9
10
SUMMARY OUTPUT
Regression Statistics
Multiple R
XXXX
R Square
XXXX
Adjusted R Square
0.7904
Standard Error
0.0754
Observations
20
19
20
ANOVA
Regression
Residual
Total
df
1
18
19
Intercept
Diuretic (milligrams)
SS
0.4125
0.1022
0.5147
MS
0.4125
0.0057
Coefficients
0.0382
1.1639
F
72.6458
Standard Error
0.0710
0.1366
Significance F
0.0000
t Stat
0.5387
8.5233
P-value
0.5967
0.0000
18. What is the correlation between these two variables?
A.
.856
B.
-.856
C.
.0754
D.
.7904
E.
.8952*
19. What is the intercept of the least squares line?
A.
253,57
B.
–1.042
C.
1.1639
D.
0.0382 *
E.
0.4125
20. What percentage of the variation in weight loss is explained by its regression on diuretic
amount?
A. 45
B. 69
C. 75
D. 19.86
E. 80.14*
21. According to the least squares regression from this sample, when the diuretic increases by 1
milligram, the weight loss will:
A. Increase by 1.1639 pounds*
B. Decrease by 1.1639 pounds
C. Increase by .0382 pounds
D. Decrease by 0.0382 pounds
E. Increase by 1.223 pounds
22. Based on the outcome of the hypothesis test for the slope of the regression line at the 5%
significance level, we can conclude that:
A. There is insufficient evidence that there is a relationship between weight loss and
daily dose of the diuretic.
B. There is sufficient evidence that the slope of the regression line is equal to zero.
C. There is insufficient evidence that the slope of the regression line is positive.
D. There is sufficient evidence that there is a relationship of weight loss and daily dose
of the diuretic. *
E. Inconclusive.
23. Assuming the confidence interval for the slope is [0.8770 to 1.4508], we can conclude that:
A. There is sufficient evidence that there is a relationship between weight loss and daily
dose of the diuretic.*
B. There is insufficient evidence that there is a relationship between weight loss and
daily dose of the diuretic.
C. There is sufficient evidence that the slope of the regression line is equal to zero.
D. There is insufficient evidence that the slope of the regression line is positive.
E. Inconclusive.
Use the following information to answer the next five questions.
The personnel manager of a large insurance company wishes to evaluate the leadership of
supervisors, mid-level managers and upper-level managers. 10 persons from each management
level were sampled. Is there a difference on the average of the leadership scores for the three
groups? Leadership indices and ANOVA table are as follows:
Supervisor
Mid-Manager
Upper
Manager
16
34
21
32
35
41
21
15
20
21
40
29
28
49
.
.
.
35
31
33
48
38
37
42
45
25
36
29
26
27
Count
10
10
10
Sum
256
352
353
Average
25.6
35.2
35.3
Variance
81.82222
40.84444
68.01111
SS
620.8667
1716.10
XXXX
df
X
27
29
MS
XXXX
XXXX
F
XXXX
SUMMARY
Groups
Supervisor
Mid-Manager
Upper Manager
ANOVA
Source of Variation
Between Groups
Within Groups
Total
P-value
0.0155
F crit
3.3541
24. Which of the following would be the appropriate null hypothesis for testing the claim that
there is significant difference of leadership scores among these three management levels?
A. Ho: At least one pair of μ1, μ2, μ3 is different
B. Ho: μ1  μ2 μ3
C. Ho: μ1 > μ2 > μ3
D. Ho: μ1 < μ2 < μ3
E. Ho: μ1 = μ2 = μ3 *
25. How much is the total variation among the leadership scores?
A. 1716
B. 2337*
C. 621
D. 310
E. 63
26. What is the calculated value of the test statistic?
A. 19.45
B. 3.40
C.4.88*
D. 3.35
E. 2.54
27. What is the critical value of the test statistic? Use a = 0.05.
A. 4.48
B. 3.35*
C. 3.13
D. 3.60
E. 2.54
28. Using a = 0.05 and assuming the calculated F value is 4.88, what is the conclusion of this
ANOVA test?
A. There is insufficient information to decide whether the leadership scores are different.
B. Fail to reject H0, conclude the mean leadership scores are different.
C. Fail to reject H0, conclude there is insufficient evidence for the mean leadership
scores being different.
D. Reject H0, conclude the mean leadership scores are different.*
E. Reject H0, conclude the mean leadership scores are equal.
Use the following information to answer the next four questions.
To predict the sales prices of a used Mustang GT, the following data from the past sales records
for the car were collected - the car’s age, condition, and mileage and seller (whether the seller is
an individual or a dealer). The dummy variable X3 is set equal to 0 if the car is in poor condition,
1 if not. The dummy variable X4 is set equal to 1 if the seller is a dealer and 0 if not (i.e., if the
seller is an individual). The data was analyzed using the multiple regression module of Excel,
and partial results are given, following the data. Please complete the Tables only to the extent
required to answer the subsequent questions.
sales
Price(Y)
Age (in
Years) X1
Mileage(in
1000s) X2
4103
3803
4098
6603
5091
5003
9
9
8
7
7
7
74
.
.
51
54
78
Condition
(Excellent, Poor)
X3
1
0
0
0
0
0
Dealer or individual
X4
0
0
0
1
0
0
3903
7903
7398
4803
8553
7903
7898
7579
7553
5903
10798
10778
10698
9603
9098
8098
7553
15453
13068
7
6
6
6
5
5
5
5
5
5
4
4
4
4
4
4
4
3
3
110
65
70
55
59
62
66
55
59
70
48
32
48
50
50
51
69
24
27
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.938236
R Square
0.880287
Adjusted R Square 0.856344
Standard Error
1110.74
Observations
25
ANOVA
df
Regression
Residual
Total
XX
20
24
SS
181442155.2
24674887.4
206117042.6
MS
45360538.8
1233744.37
Coefficients Standard Error
Intercept
14655.61
888.3083
Age (in Years) X1
-1070.16
197.5215
Mileage(in 1000s) X2
-24.90
16.0507
Condition (Excellent, Poor) X3
-824.58
537.3320
Dealer or individual X4
1976.33
554.5758
F
36.766562
t Stat
16.4983
-5.4180
-1.5512
-1.5346
3.5637
Significance F
5.9261E-09
P-value Lower 95% Upper 95%
0.0000
12802.6
16508.6
XXXX
-1482.2
-658.1
0.1365
-58.4
8.6
0.1406
-1945.4
296.3
0.0019
819.5
3133.2
29. If we wish to determine whether Mileage (variable X2) has a significant effect on the sales
price, what is the calculated value of the test statistic?
A. 16.4983
B. -5.4180
C. -1.5512*
D. -1.5346
E. 3.5637
30. What is the p value, associated with the calculated value of the test statistic for the variable
age (X1)?
A. p-value < .01*
B. 0.01 < p-value < 0.025
C. 0.025 < p-value < 0.05
D. 0.05 < p-value < 0.10
E. p-value > 0.10
31. What is the Upper limit of the 95% confidence interval for 3, the coefficient of "condition”?
A.
B.
C.
D.
E.
16508.6
-658.1
8.6
296.3*
3133.2
32. What is the predicted sales price of a 5 year old car in excellent condition, having a mileage
of 90,000, sold by an individual?
A.
B.
C.
D.
E.
$ 9,040
$ 6,239*
$ 3,154
$ 5,903
$ 2,991
33. What are the degrees of freedom for regression?
A.
B.
C.
D.
E.
24
20
4*
5
6
*********************** Enjoy your summer break ***********************