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Statistics and Research Methodology
Fall 2015
Practice Final Exam
1. The credit manager of a large department store claims that the mean balance for the store’s
charge account customers is $410. An independent auditor selects a random sample of 18
accounts and finds a mean balance of $511.33 and a standard deviation of $183.75. If the
manager’s claim is not supported by these data, the auditor intends to examine all charge
account balances. If the population of account balances is assumed to be approximately
normally distributed, what action should the auditor take? Use α = 0.05.
2. Many grocery stores and large retailers such as Wal-Mart and K-Mart have installed selfcheckout systems so shoppers can scan their own items and cash out themselves. How do
customers like this service and how often do they use it? Listed below is the number of
customers using the service for a sample of 15 days at a Wal-Mart store (Data: Customers).
120
108
112
97
120
114
118
118
108
117
91
118
92
104
104
Is it reasonable to conclude that the mean number of customers using the self-checkout system
is more than 100 per day? Use the 0.05 significance level.
3. One factor in low productivity is the amount of time wasted by workers. Wasted time includes
time spent cleaning up mistakes, waiting for more material and equipment, and performing
any other activity not related to production. In a project designed to examine the problem, an
operations-management consultant took a survey of 25 workers in companies that were classified as successful (on the basis of their latest annual profits) and 30 workers from unsuccessful
companies. The amount of time (in hours) wasted during a standard 40-hour workweek was
recorded for each worker (Data: Productivity). Do these data provide enough evidence at the
1% significance level to infer that the amount of time wasted in unsuccessful firms exceeds
that of successful ones?
4. The Global Business Travel Association reported the domestic airfare for business travel for
the current year and the previous year (INC. Magazine, February 2012). Given is a sample of
12 flights with their domestic airfares shown for both years (Data: Airfare).
(a) At the 0.05 level of significance, test whether there has been a significant increase in the
mean domestic airfare for business travel for the one-year period.
(b) Why the study has been designed this way?
1
5. A sample of 40 investment customers serviced by an account manager are found to have
had an average of $23,000 in transactions during the past year, with a standard deviation
of $8500. A sample of 30 customers serviced by another account manager averaged $28,000
in transactions, with a standard deviation of $11,000. At the 0.05 level of significance, test
whether the population means could be equal for customers serviced by the two account
managers.
6. A study reported in the Journal of Small Business Management concluded that self-employed
individuals do not experience higher job satisfaction than individuals who are not self-employed.
In this study, job satisfaction is measured; a higher score on this scale indicates a higher degree of job satisfaction. The approach was used to measure the job satisfaction for lawyers,
physical therapists and systems analysts. The results obtained for a sample of 10 individuals
from each profession are recorded (Data: Satisfaction). Use α = 0.05.
(a) Test for any difference in the job satisfaction among the three professions?
(b) Use Tukey’s procedure to order the mean satisfaction of the three professions.
7. An engineering student who is about to graduate decided to survey various firms in Silicon
Valley to see which offered the best chance for early promotion and career advancement. He
surveyed 30 small firms (size level is based on gross revenues), 30 medium-sized firms, and
30 large firms, and determined how much time must elapse before an average engineer can
receive a promotion (Data: Firms).
(a) At 5% level, can the engineering student conclude that speed of promotion varies between
the three sizes of engineering firms?
(b) Determine which firms, if any, differ at the 5% level. Which firm would you recommend
to the student? Explain.
(c) What would be your conclusion at 1% level?
8. A newspaper publisher trying to pinpoint his market’s characteristics wondered whether the
way people read a newspaper is related to the reader’s educational level. A survey asked adult
readers which section of the paper they read first and asked to report their highest educational
level (Data: newspapers). These data were recorded (column 1 = First section read where 1
= Front page, 2 = Sports, 3 = Editorial, and 4 = Other) and column 2 = Educational level
where 1 = Did not complete high school, 2 = High school graduate, 3 = University or college
graduate, and 4 = Postgraduate degree). At the 0.05 level of significance, what do these data
tell the publisher about how educational level affects the way adults read the newspaper?
2
9. Management of a soft-drink bottling company wants to develop a method for allocating delivery costs to customers. Although one cost clearly relates to travel time within a particular
route, another variable cost reflects the time required to unload the cases of soft drink at the
delivery point. A sample of 20 deliveries within a territory was selected. The delivery times
and the numbers of cases delivered were recorded (Data: Delivery).
(a) Construct a scatter plot of delivery time and number of cases delivered. Comment on
the graph.
(b) Find and interpret the correlation coefficient between delivery time and number of cases
delivered.
(c) Estimate the regression model to predict delivery time, based on the number of cases
delivered.
(d) Interpret the meaning the regression coefficients.
(e) Determine the coefficient of determination and explain its meaning in this problem.
(f) At the 0.05 level of significance, is there evidence of a linear relationship between delivery
time and the number of cases delivered?
(g) Predict the delivery time for 150 cases of soft drink.
(h) Predict with 95% confidence the mean delivery time for 150 cases of soft drink.
(i) Predict with 95% confidence the delivery time for a single delivery of 150 cases of soft
drink.
(j) Should you use the model to predict the delivery time for a customer who is receiving
500 cases of soft drink? Why or why not?
(k) The next deliver contains 200 cases and the manager claims that this delivery will be
done in 45 minutes. How accurate is this claim? Justify your answer.
10. The owner of a moving company typically has his most experienced manager predict the total
number of labor hours that will be required to complete an upcoming move. This approach
has proved useful in the past, but the owner has the business objective of developing a more
accurate method of predicting labor hours. In a preliminary effort to provide a more accurate
method, the owner has decided to use the number of cubic feet moved (x1 ), the number
of pieces of large furniture (x2 ) and whether there is an elevator in the apartment building
(x3 = 1 if yes, x3 = 0 if no) as the independent variables and has collected data for 36 moves
(Data: Moving).
(a) Find the estimated regression equation for predicting labor hours, using the number of
cubic feet moved, the number of pieces of large furniture and whether there is an elevator.
3
(b) Interpret the regression coefficients.
(c) Determine whether there is a significant relationship between labor hours and the three
independent variables at the 0.05 level of significance.
(d) At the 0.05 level of significance, test whether the number of pieces of large furniture
makes a significant contribution to the regression model.
(e) At the 0.05 level of significance, test whether the number of cubic feet moved can be
dropped from the regression model.
(f) At the 0.05 level of significance, test whether having elevator in the apartment building
has an effect on the total number of labor hours.
(g) Find and interpret the coefficient of multiple determination in this problem.
(h) Predict the labor hours for moving 500 cubic feet with two large pieces of furniture in
an apartment building that has an elevator.
(i) Predict with 95% confidence the labor hours for moving 500 cubic feet with two large
pieces of furniture in an apartment building that has an elevator.
(j) Is there any signs of multicollinearity problem? Explain.
(k) Discuss the need for other independent variables that could be added to the model. What
additional variables might be helpful?
11. For each of the following scenarios, identify each of the following components, giving reasons:
• The purpose of the study
• The research objective(s)/Hypotheses/Questions
• Research Methodology:
– Research design (Research strategy and type of study)
– Participants
– Sampling Design
– Research Instrument
– Data Collection Method
– Data Analysis
(a) Maryam, the owner of a small business (a woman’s dress boutique), has invited a consultant to tell her how she is different from similar small business within a 60-km radius,
in regard to her usage of the most modern computer technology, sales volume, profit
margin, and staff training.
4
(b) You are the administrative assistant for a division chief in a large holding company that
owns several hotels and theme parks. You and the division chief have just come from
the CEO’s office, where you were informed that the guest complaints related to housekeeping and employee attitude are increasing. Your on-site managers have mentioned
some tension among the workers but have not considered it unusual. The CEO and your
division chief instruct you to investigate.
(c) Assume you are a manufacturer of small kitchen electrics, like Hamilton Beach/Proctor
Silex, and you want to determine if some innovative designs with unusual shapes and
colors developed for the European market could be successfully marketed in the UAE
market.
(d) While Chrysler’s minivans, pickups, and sport utility vehicles take a big share of the
truck market, its cars trail behind those of GM, Ford, Honda, and Toyota.
(e) Companies benefit through employee loyalty. Crude downsizing in organizations during
the recession crushed the loyalty of millions. The economic benefits of loyalty embrace
lower recruitment and training costs, higher productivity of workers, customer satisfaction, and boost the morale of fresh recruits. In order that these benefits may not be
lost, some companies, while downsizing, try various gimmicks. Flex leave, for instance,
is one. This helps employees receive 20% of their salary, plus employer-provided benefits
while they take a 6-12 month sabbatical, with a call option on their services. Others try
alternatives like more communication, hand holding, and the like.
5
Customers
120
108
112
97
120
114
118
118
108
117
91
118
92
104
104
Successful Unsuccessful
5
7,1
6,7
4,1
4,7
4,5
4,7
10,8
6,6
10,8
3,8
14,1
4,5
6,7
5,3
6,5
2,5
10,7
4,8
7,9
5,9
7,4
5,5
5,9
2,6
2,9
4,1
9,1
7,4
8
5,8
9,3
3,9
7,5
7,3
7,1
4,1
2,4
3,8
9,7
5,6
11,4
3,4
8,6
5,9
6,9
3,8
4,3
5
8,1
8,6
3,2
3,8
11,5
8,9
Flight
1
2
3
4
5
6
7
8
9
10
11
12
Current
345
526
420
216
285
405
635
710
605
517
570
610
Previous
315
463
462
206
275
432
585
650
545
547
508
580
Lawyers Physical Therapists
44
55
42
78
74
80
42
86
53
60
50
59
45
62
48
52
64
55
38
50
Systems Analysts
44
73
71
60
64
66
41
55
76
62
Small
28
55
43
41
63
52
53
42
16
57
73
58
31
61
51
45
58
61
49
71
65
45
84
44
59
54
67
53
67
49
Medium
56
56
50
65
53
60
47
66
56
36
38
30
43
46
68
66
55
53
23
38
48
41
47
50
45
49
53
32
77
34
Large
55
59
57
58
37
42
45
51
14
46
28
46
41
44
32
48
33
34
41
41
37
58
52
52
40
52
52
57
21
57
Section Education
4
2
2
2
4
2
4
3
4
2
1
4
1
3
1
2
4
1
2
2
2
3
4
3
2
2
4
1
2
3
3
3
4
3
1
3
3
3
4
2
1
4
2
4
1
2
2
2
1
2
2
1
2
2
3
3
1
4
3
3
1
2
1
4
2
4
3
3
4
2
3
3
1
4
1
2
2
2
2
3
1
3
2
1
3
3
4
2
3
3
4
2
2
1
4
3
1
2
4
3
3
2
2
3
4
4
2
1
3
4
3
2
4
1
1
4
2
2
3
3
2
3
3
1
4
4
1
4
4
4
1
1
2
2
1
3
4
2
3
2
4
2
3
2
2
2
2
3
2
3
4
2
2
3
3
3
1
3
1
2
3
3
1
1
1
2
2
1
3
4
4
2
2
3
3
3
2
3
3
1
1
3
4
2
1
3
2
4
4
2
4
4
2
3
2
2
1
1
1
3
3
2
3
4
4
4
3
1
3
4
1
4
1
4
4
2
3
2
1
1
2
2
2
1
3
2
3
1
2
1
3
1
3
1
2
2
2
2
2
2
3
2
1
3
4
2
2
3
2
2
3
2
3
2
3
2
3
2
2
2
2
1
1
4
2
3
3
1
1
1
3
4
3
4
1
3
1
3
4
2
4
4
3
3
4
4
3
3
3
2
4
3
4
4
1
1
4
2
4
1
3
3
3
3
3
2
2
2
2
4
2
1
2
2
3
2
3
3
3
3
3
3
2
3
2
3
4
2
3
4
4
3
2
4
3
3
2
2
2
4
1
3
3
3
2
3
4
2
3
3
3
4
1
1
1
3
1
1
2
3
1
3
2
3
4
2
4
3
3
3
2
3
3
2
3
1
2
3
3
3
2
1
4
1
3
1
2
1
3
4
4
1
3
4
4
1
4
4
3
4
3
1
3
1
1
3
3
2
4
4
4
4
2
2
2
2
2
4
3
1
1
2
4
1
4
2
2
2
3
2
3
3
2
2
3
4
2
2
3
4
3
3
2
3
2
4
3
3
4
4
4
2
3
2
2
2
4
2
2
1
2
1
2
2
1
3
3
1
3
3
2
1
3
3
4
1
3
2
4
4
2
1
1
3
4
3
2
2
1
3
1
3
2
1
1
4
1
4
2
3
4
1
4
3
4
3
2
4
4
4
2
1
2
1
1
3
3
2
2
3
4
4
3
4
2
1
2
3
2
2
3
2
3
3
3
3
2
3
1
1
3
2
3
2
2
3
3
2
3
3
4
2
2
2
1
3
3
2
2
2
3
1
3
2
4
2
3
4
3
3
2
4
2
3
1
3
2
3
1
2
1
3
2
4
4
3
1
2
1
4
2
1
2
4
3
2
2
1
4
3
3
3
2
2
3
4
3
3
3
3
3
2
3
2
1
3
2
2
2
2
4
2
1
2
3
2
Cases
52
64
73
85
95
103
116
121
143
157
161
184
202
218
243
254
267
275
287
298
Time
32,1
34,8
36,2
37,8
37,8
39,7
38,5
41,9
44,2
47,1
43
49,4
57,2
56,8
60,6
61,2
58,2
63,1
65,6
67,3
Y
24,00
13,50
26,25
25,00
9,00
20,00
22,00
11,25
50,00
12,00
38,75
40,00
19,50
18,00
28,00
27,00
21,00
15,00
25,00
45,00
29,00
21,00
22,00
16,50
37,00
32,00
34,00
25,00
31,00
24,00
40,00
27,00
18,00
62,50
53,75
79,50
X1
545
400
562
540
220
344
569
340
900
285
865
831
344
360
750
650
415
275
557
1028
793
523
564
312
757
600
796
577
500
695
1054
486
442
1249
995
1397
X2
3
2
2
2
1
3
2
1
6
1
4
4
3
2
3
2
2
2
2
5
4
3
3
2
3
3
3
3
4
3
4
3
2
5
6
7
X3
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
0
Regression Analysis
r² 0,725
n 21
r 0,851
k 1
Std. Error 40513,995
Dep. Var. Average Monthly Sales $
ANOVA table
df
MS
F
p-value
Regression ################
Source
SS
1
###############
50,10
9,83E-07
Residual ################
19
###############
Total ################
20
Regression output
confidence interval
variables
coefficients
std. error
t (df=19)
p-value
95% lower
95% upper
Intercept
171.205,8279
59.846,1252
2,861
,0100
45.946,4483
296.465,2075
store size (sq.ft)
25,3160
3,5767
7,078
9,83E-07
17,8299
32,8022
Predicted values for: Average Monthly Sales $
95% Confidence Interval
store size (sq.ft)
Predicted
lower
15.000
550.946,445
529.110,736
upper
95% Prediction Interval
lower
upper
Leverage
572.782,154 ########
638.509,507
0,066
Hypothesis Test: Independent Groups (t-test, pooled variance)
Men
26,3283
6,3700
12
Women
16,9325 mean
4,3765 std. dev.
12 n
22
9,39583
29,86520
5,46491
2,23104
0
df
difference (Men – Women)
pooled variance
pooled std. dev.
standard error of difference
hypothesized difference
4,211 t
,0002 p-value (one-tailed, upper)
4,76894 confidence interval 95.% lower
14,02272 confidence interval 95.% upper
4,62689 margin of error
Hypothesis Test: Paired Observations
0,000
48,167
45,333
2,833
3,927
1,134
12
hypothesized value
mean after
mean Before
mean difference (after – Before)
std. dev.
std. error
n
11 df
2,499 t
,0148 p-value (one-tailed, upper)
Hypothesis Test: Paired Observations
0,000
48,167
45,333
2,833
3,927
1,134
12
11
hypothesized value
mean after
mean Before
mean difference (after – Before)
std. dev.
std. error
n
df
2,499 t
,0148 p-value (one-tailed, upper)
0,338 confidence interval 95.% lower
5,329 confidence interval 95.% upper
2,495 margin of error
Regression Analysis
R² 0,771
Adjusted R² 0,718
R 0,878
Std. Error
n
k
Dep. Var.
ANOVA table
Source
Regression
Residual
Total
SS
336.488,0039
99.799,0549
436.287,0588
Regression output
variables
coefficients
Intercept
-16,0752
gender
248,6859
Quality of work score
1,7700
experience (years)
1,7205
87,618
17
3
salary increase $
df
3
13
16
std. error
70,0168
44,9951
0,9043
9,3894
MS
112.162,6680
7.676,8504
F
14,61
p-value
,0002
confidence interval
t (df=13) p-value 95% lower 95% upper
-0,230
,8220 -167,3374
135,1870
5,527
,0001 151,4799
345,8919
1,957
,0721
-0,1835
3,7236
0,183
,8574 -18,5641
22,0052
Regression Analysis

Adjusted R²
R
Std. Error
ANOVA table
Source
Regression
Residual
Total
SS
336.488,0039
99.799,0549
436.287,0588
Regression output
variables
coefficients
Intercept
232,6107
gender
-248,6859
Quality of work score
1,7700
experience (years)
1,7205
0,771
0,718
0,878
87,618
df
3
13
16
std. error
82,6806
44,9951
0,9043
9,3894
n 17
k 3
Dep. Var. salary increase $
MS
112.162,6680
7.676,8504
F
14,61
p-value
,0002
confidence interval
t (df=13) p-value 95% lower 95% upper
2,813
,0146
53,9902
411,2312
-5,527
,0001 -345,8919 -151,4799
1,957
,0721
-0,1835
3,7236
0,183
,8574 -18,5641
22,0052
Regression Analysis

Adjusted R²
R
Std. Error
ANOVA table
Source
Regression
Residual
Total
SS
339.392,8681
96.894,1908
436.287,0588
0,778
0,727
0,882
86,333
df
3
13
16
n 17
k 3
Dep. Var. salary increase $
MS
113.130,9560
7.453,3993
F
15,18
p-value
,0002
Regression output
variables
coefficients
Intercept
138,4550
gender
-245,4028
Quality of work score
2,6925
experience (years)
5,5123
std. error
118,1097
44,6266
1,2930
10,1213
t (df=13) p-value
1,172
,2621
-5,499
,0001
2,082
,0576
0,545
,5952
confidence interval
95% lower 95% upper
-116,7056
393,6156
-341,8127 -148,9929
-0,1009
5,4859
-16,3534
27,3780
Regression Analysis

Adjusted R²
R
Std. Error
ANOVA table
Source
Regression
Residual
Total
0,739
0,679
0,860
93,547
SS
322.522,9436
113.764,1152
436.287,0588
Regression output
variables
coefficients
Intercept
200,6745
gender
-221,5737
Quality of work score
1,6267
experience (years)
1,5816
df
3
13
16
std. error
132,8159
60,3076
1,2243
10,9371
n 17
k 3
Dep. Var. salary increase $
MS
107.507,6479
8.751,0858
F
12,29
p-value
,0004
confidence interval
t (df=13) p-value 95% lower 95% upper
1,511
,1547 -86,2568
487,6059
-3,674
,0028 -351,8603
-91,2871
1,329
,2068
-1,0182
4,2717
0,145
,8872 -22,0467
25,2099
Regression Analysis

Adjusted R²
R
Std. Error
ANOVA table
Source
Regression
Residual
Total
0,783
0,733
0,885
85,319
SS
341.656,1267
94.630,9321
436.287,0588
Regression output
variables
coefficients
Intercept
88,4259
gender
-176,7830
Quality of work score
2,9687
experience (years)
5,8924
df
3
13
16
std. error
134,6633
61,0460
1,3620
9,9885
n 17
k 3
Dep. Var. salary increase $
MS
113.885,3756
7.279,3025
p-value
,0001
confidence interval
t (df=13) p-value 95% lower 95% upper
0,657
,5229 -202,4964
379,3483
-2,896
,0125 -308,6649
-44,9010
2,180
,0483
0,0262
5,9111
0,590
,5654 -15,6865
27,4713
Regression Analysis
R² 0,783
Adjusted R² 0,733
R 0,885
F
15,65
n 17
k 3
Std. Error 85,319
ANOVA table
Source
Regression
Residual
Total
SS
341.656,1267
94.630,9321
436.287,0588
Regression output
variables
coefficients
Intercept
-88,3570
gender
176,7830
Quality of work score
2,9687
experience (years)
5,8924
Dep. Var. salary increase $
df
3
13
16
std. error
92,4774
61,0460
1,3620
9,9885
MS
113.885,3756
7.279,3025
F
15,65
p-value
,0001
confidence interval
t (df=13) p-value 95% lower 95% upper
-0,955
,3568 -288,1422
111,4282
2,896
,0125
44,9010
308,6649
2,180
,0483
0,0262
5,9111
0,590
,5654 -15,6865
27,4713
Regression Analysis

Adjusted R²
R
Std. Error
ANOVA table
Source
Regression
Residual
Total
SS
0,783
0,733
0,885
85,319
n 17
k 3
Dep. Var. salary increase $
df
MS
F
p-value
341.656,1267
3
113.885,3756
15,65
,0001
94.630,9321
13
7.279,3025
436.287,0588
16
Regression output
confidence interval
variables
coefficients
std. error
t (df=13)
p-value
95% lower
95% upper
Intercept
-88,3570
92,4774
-0,955
,3568
-288,1422
111,4282
gender
176,7830
61,0460
2,896
,0125
44,9010
308,6649
Performance
2,9687
1,3620
2,180
,0483
0,0262
5,9111
experience
5,8924
9,9885
0,590
,5654
-15,6865
27,4713
store size (sq.ft)
Average Monthly Sales $
17400
581241
15920
538275
17440
636059
173 …
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