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EMBS4-TB11.doc – 19

Undecided

10%

After the presidential debates, a random sample of 1200 voters showed that 540 favored

the Democratic candidate; 480 were in favor of the Republican candidate; 40 were in

favor of the Independent candidate, and 140 were undecided. We want to see if the

proportion of voters has changed.

a. Compute the test statistic.

b. Use the p-value approach to test the hypotheses. Let = .05.

c. Using the critical value approach, test the hypotheses. Let = .05.

22. Last school year, in the school of Business Administration, 30% were Accounting

majors, 24% Management majors, 26% Marketing majors, and 20% Economics majors.

A sample of 300 students taken from this year’s students of the school showed the

following number of students in each major:

Major

Students

Accounting

83

Management

68

Marketing

85

Economics

64

Total

300

We want to see if there has been a significant change in the number of students in each

major.

a. Compute the test statistic.

b. Has there been any significant change in the number of students in each major

between the last school year and this school year. Use the p-value approach and let

= .05.

23. The personnel department of a large corporation reported sixty resignations during the

last year. The following table groups these resignations according to the season in which

they occurred.

Season

Number of

Resignations

Winter

10

Spring

22

Summer

19

Fall

9

Test to see if the number of resignations is uniform over the four seasons.

Let = 0.05.

24. In 2003, forty percent of the students at a major university were Business majors, 35% were

Engineering majors and the rest of the students were majoring in other fields. In a sample of

600 students from the same university taken in 2004, two hundred were Business majors,

220 were Engineering majors and the remaining students in the sample were majoring in

other fields. At 95% confidence, test to see whether there has been a significant change in

the proportions between 2003 and 2004.

25. In the last presidential election before the candidates began their major campaigns, the

percentages of registered voters who favored the various candidates were as follows.

Percentage

Republicans

34

Democrats

43

Independents

23

After the major campaigns began, a random sample of 400 voters showed that 172

favored the Republican candidate; 164 were in favor of the Democratic candidate; and 64

favored the Independent candidate. Test with = .01 to see if the proportion of voters

who favored the various candidates changed.

26. Before the rush began for Christmas shopping, a department store had noted that the

percentage of its customers who use the store’s credit card, the percentage of those who

use a major credit card, and the percentage of those who pay cash are the same. During

the Christmas rush in a sample of 150 shoppers, 46 used the store’s credit card; 43 used a

major credit card; and 61 paid cash. With = 0.05, test to see if the methods of payment

have changed during the Christmas rush.

27. A major automobile manufacturer claimed that the frequencies of repairs on all five

models of its cars are the same. A sample of 200 repair services showed the following

frequencies on the various makes of cars.

Model of Car

Frequency

A

32

B

45

C

43

D

34

E

46

At = 0.05, test the manufacturer’s claim.

28. A lottery is conducted that involves the random selection of numbers from 0 to 4. To

make sure that the lottery is fair, a sample of 250 was taken. The following results were

obtained.

Value

Frequency

0

40

1

45

2

55

3

60

4

50

a. State the null and alternative hypotheses to be tested.

b. Compute the test statistic.

c. The null hypothesis is to be tested at the 5% level of significance. Determine the

critical value from the table.

d. What do you conclude about the fairness of this lottery?

29. The makers of Compute-All know that in the past, 40% of their sales were from people

under 30 years old, 45% of their sales were from people who are between 30 and 50 years

old, and 15% of their sales were from people who are over 50 years old. A sample of 300

customers was taken to see if the market shares had changed. In the sample, 100 of the

people were under 30 years old, 150 people were between 30 and 50 years old, and 50

people were over 50 years old.

a. State the null and alternative hypotheses to be tested.

b. Compute the test statistic.

c. The null hypothesis is to be tested at the 1% level of significance. Determine the

critical value from the table.

d. What do you conclude?

30. The following table shows the results of a recent study regarding the gender of

individuals and their selected field of study.

Field of Study

Male

Female

Total

Medicine

80

40

120

Business

60

20

80

Engineering

160

40

200

Total

300

100

400

We want to determine if the selected field of study is independent of gender.

a. Compute the test statistic.

b. Using the p-value approach at 90% confidence, test to see if the field of study is

independent of gender.

c. Using the critical method approach at 90% confidence, test for the independence of

major and gender.

31. Shown below is 3 x 2 contingency table with observed values from a sample of 1,500. At

95% confidence, test for independence of the row and column factors.

Column Factor

Row Factor

X

Y

Total

A

450

300

750

B

300

300

600

C

100

50

150

Total

850

650

1,500

32. Shown below is 2 x 3 contingency table with observed values from a sample of 500. At

95% confidence using the critical value approach, test for independence of the row and

column factors.

Column Factor

Row Factor

X

Y

Z

A

40

50

110

B

60

100

140

33. A sample of 150 individuals (males and females) was surveyed, and the individuals were

asked to indicate their yearly incomes. Their incomes were categorized as follows.

Category 1 $20,000 up to $40,000

Category 2 $40,000 up to $60,000

Category 3 $60,000 up to $80,000

The results of the survey are shown below.

Income Category

Male

Female

Category 1

10

30

Category 2

35

15

Category 3

15

45

We want to determine if yearly income is independent of gender.

a. Compute the test statistic.

b. Using the p-value approach, test to determine if yearly income is independent of

gender.

34. A group of 2000 individuals from 3 different cities were asked whether they owned a

foreign or a domestic car. The following contingency table shows the results of the

survey.

City

Type of Car

Detroit

Atlanta

Denver

Total

Domestic

80

200

520

800

Foreign

120

600

480

1200

Total

200

800

1000

2000

At = 0.05 using the p-value approach, test to determine if the type of car purchased is

independent of the city in which the purchasers live.

35. Dr. Sherri Brock’s diet pills are supposed to cause significant weight loss. The following

table shows the results of a recent study where some individuals took the diet pills and

some did not.

Diet Pills

No Diet Pills

Total

No Weight Loss

80

20

100

Weight Loss

100

100

200

Total

180

120

300

We want to see if losing weight is independent of taking the diet pills.

a. Compute the test statistic.

b. Using the p-value approach at 95% confidence, test to determine if weight loss is

independent on taking the pill.

c. Use the critical method approach and test for independence.

36. Five hundred randomly selected automobile owners were questioned on the main reason

they had purchased their current automobile. The results are given below.

Styling

Engineering

Fuel Economy

Total

Male

70

130

150

350

Female

30

20

100

150

100

150

250

500

a. State the null and alternative hypotheses for a contingency table test.

b. State the decision rule for the critical value approach. Let = 0.10.

c. Calculate the 2 test statistic.

d. Give your conclusion for this test.

37. A group of 500 individuals were asked to cast their votes regarding a particular issue of

the Equal Rights Amendment. The following contingency table shows the results of the

votes:

Sex

Favor

Undecided

Oppose

Total

Female

180

80

40

300

Male

150

20

30

200

Total

330

100

70

500

At = .05 using the p–value approach, test to determine if the votes cast were

independent of the sex of the individuals.

38. Two hundred fifty managers with degrees in business administration indicated their fields

of concentration as shown below.

Major

Top Management

Middle Management

Total

Management

65

60

125

Marketing

30

20

50

Accounting

25

50

75

Total

120

130

250

At = .01 using the p–value approach, test to determine if the position in management is

independent of the major of concentration.

39. From a poll of 800 television viewers, the following data have been accumulated as to

their levels of education and their preference of television stations.

Level of Education

High School

Bachelor

Graduate

Total

Public Broadcasting

110

190

100

400

Commercial Stations

80

220

100

400

Total

190

410

200

800

Test at = .05 to determine if the selection of a TV station is dependent upon the level of

education. Use the p-value approach.

40. The data below represents the fields of specialization for a randomly selected sample of

undergraduate students. We want to determine whether there is a significant difference in

the fields of specialization between regions of the country.

Northeast

Midwest

South

West

Total

Business

54

65

28

93

240

Engineering

15

24

8

33

80

Liberal Arts

65

84

33

98

280

Fine Arts

13

15

7

25

60

Health Sciences

3

12

4

21

40

150

200

80

270

700

a. Determine the critical value of the chi-square (2) for this test of independence.

b. Calculate the value of the test statistic.

c. What is the conclusion for this test? Let = .05.

41. A manufacturing company wants to estimate the difference in the proportion of defective

parts between two machines. Independent random samples of parts are taken from both

machines. The results follow. Use Excel to estimate the difference in the proportion of

defective parts between two machines with a 99% level of confidence.

Machine 1

Machine 2

Yes

Yes

No

No

No

No

No

Yes

No

No

Yes

No

No

No

No

No

No

No

No

Yes

No

No

No

No

No

No

No

Yes

No

No

No

No

No

No

Yes

No

No

No

No

Yes

No

No

No

Yes

No

No

No

No

No

No

No

No

Yes

No

No

No

No

Yes

No

No

42. A company gives a test to prospective employees before granting an interview. A

researcher hypothesizes that men tend to answer one particular test question correctly

more often than women. Independent samples of both groups are given the test. The

results for the question of interest follow. Does the data provide sufficient evidence to

conclude that the proportion of correct answers given by men is greater than that of

women? Use Excel to conduct the appropriate test at = .05.

Men

Women

Yes

Yes

Yes

Yes

No

No

Yes

Yes

No

Yes

Yes

No

Yes

No

No

Yes

No

No

No

Yes

No

Yes

Yes

No

Yes

Yes

No

Yes

No

No

Yes

Yes

No

No

Yes

No

No

Yes

No

Yes

No

No

No

Yes

No

No

No

No

Yes

No

No

No

Yes

No

No

Yes

No

Yes

Yes

No

43. The results of recent polls on presidential approval ratings are shown below.

Approved of President in January

Approved of President in July

Yes

Yes

Yes

Yes

No

No

No

Yes

No

Yes

Yes

No

No

No

No

Yes

No

No

No

Yes

No

Yes

Yes

No

No

Yes

No

Yes

No

No

Yes

Yes

No

No

Yes

No

Yes

Yes

No

Yes

No

No

No

Yes

No

No

No

No

No

No

No

No

Yes

No

Yes

Yes

No

Yes

Yes

No

Does the data provide sufficient evidence to conclude that the presidential approval

ratings differ between the two months? Use Excel to conduct the appropriate test at =

.05.

44. During “sweeps week” last year, the viewing audience was distributed as follows: 36%

NBC, 22% ABC, 24% CBS, and 18% FOX. This year during “sweeps week” a sample

of 50 homes yielded the following data. Use Excel to test at = .05 to determine if the

audience proportions have changed.

ABC

FOX

ABC

FOX

ABC

ABC

CBS

NBC

FOX

FOX

NBC

ABC

CBS

ABC

NBC

NBC

NBC

CBS

FOX

ABC

ABC

FOX

NBC

CBS

CBS

NBC

NBC

ABC

FOX

FOX

NBC

NBC

NBC

NBC

FOX

ABC

FOX

NBC

FOX

CBS

CBS

CBS

FOX

FOX

NBC

CBS

FOX

CBS

FOX

NBC

45. Members of a focus group stated their preferences between three possible slogans. The

results follow. Use Excel to test at = .05 to determine any difference in preference

among the three slogans.

Slogan Preferences

A

A

C

C

B

C

B

B

A

A

B

C

A

B

C

C

C

C

B

B

C

B

C

C

A

A

A

C

A

B

46. A study of wage discrimination at a local store compared employees’ race and their

status. Partial results of the study follow. Use Excel and test at = .05 to determine if

gender is independent of status.

Worker

Race

Status

Worker

Race

Status

1

white

manager

26

non-white

associate

2

non-white

associate

27

white

district manager

3

white

district

manager

28

non-white

manager

4

white

manager

29

white

associate

5

white

manager

30

non-white

district manager

6

non-white

associate

31

non-white

district manager

7

non-white

associate

32

white

district manager

8

white

associate

33

white

district manager

9

non-white

associate

34

non-white

associate

10

white

manager

35

white

district manager

11

non-white

manager

36

non-white

associate

12

non-white

associate

37

non-white

manager

13

white

associate

38

non-white

associate

14

non-white

associate

39

white

district manager

15

white

district

manager

40

non-white

associate

16

white

district

manager

41

non-white

manager

17

non-white

associate

42

non-white

district manager

18

non-white

associate

43

white

manager

19

white

associate

44

white

district manager

20

non-white

manager

45

non-white

associate

21

white

district

manager

46

non-white

associate

22

non-white

district

manager

47

non-white

district manager

23

non-white

manager

48

white

manager

24

non-white

associate

49

non-white

manager

25

non-white

associate

50

non-white

associate

47. A movie based on a best-selling novel was recently released. Six hundred viewers of the

movie, 235 of whom had previously read the novel, were asked to rate the quality of the

movie. The survey showed that 141 of the novel readers gave the movie a rating of

excellent, while 248 of the non-readers gave the movie an excellent rating.

a. Develop an interval estimate of the difference between the proportions of the two

populations, using a .05 level of significance, as the basis for your decision.

b. Can we conclude, on the basis of a hypothesis test about p1 – p2, that the

proportion of the non-readers of the novel who thought the movie was excellent

is greater than the proportion of readers of the novel who thought the movie was

excellent? Use a .05 level of significance. (Hint: this is a one-tailed test.)

48. Employee panel preferences for three proposed company logo designs follow.

Logo Design

A

B

C

Number of Employees Preferring Design

78

59

66

Use

= .05 and test to determine any difference in preference among the three logo

designs.

49. City planners are evaluating three proposed alternatives for relieving the growing traffic

congestion on a north-south highway in a booming city. The proposed alternatives are:

(1) designate high-occupancy vehicle (HOV) lanes on the existing highway, (2) construct

a new, parallel highway, and (3) construct a light (passenger) rail system.

In an analysis of the three proposals, a citizen group has raised the question of whether

preferences for the three alternatives differ among residents near the highway and non-

residents. A test of independence will address this question, with the hypotheses being:

H0: Proposal preference is independent of the residency status of the individual

Ha: Proposal preference is not independent of the residency status of the individual

A simple random sample of 500 individuals has been selected. The crosstabulation of the

residency statuses and proposal preferences of the individuals sampled is shown below.

Residency Status

HOV Lane

New Highway

Light Rail

Nearby resident

110

45

70

Distant resident

140

75

60

Conduct a test of independence using

= .05 to address the question of whether

residency status is independent of the proposal preference.

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