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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

R²

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

R²

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

R²

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

R²

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

R²

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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