23. A survey of 1500 Queenslanders reveals that 945 believe there is too much violence on television. In a
survey of 1500 Western Australians, 810 believe that there is too much television violence.
Can we infer at the 99% significance level that the proportions of Queenslanders and Western
Australians who believe that there is too much violence on television differ?
24. A survey of 1500 Queenslanders reveals that 945 believe there is too much violence on television. In a
survey of 1500 Western Australians, 810 believe that there is too much television violence.
a. Estimate with 99% confidence the difference between the proportions of Queenslanders and
Western Australians who believe that there is too much violence on television.
b. Briefly explain what the interval estimate in part a. tells you.
25. The owner of a service station wants to determine whether the owners of new cars (two years old or
less) change their cars’ oil more frequently than owners of older cars (more than two years old). From
his records, he takes a random sample of 10 new cars and 10 older cars and determines the number of
times the oil was changed for each in the last 12 months. The data are shown below.
Frequency of oil changes in the past 12 months
New car owners
Old car owners
6
4
3
2
3
1
3
2
4
3
3
2
6
2
5
3
5
2
4
1
Do these data allow the service station owner to infer at the 10% significance level that new car
owners change their cars’ oil more frequently than older car owners?
26. Ten functionally illiterate adults were given an experimental one-week crash course in reading. Each
of the 10 was given a reading test prior to the course and another test after the course. The results are
shown below.
Adult
1
2
3
4
5
6
7
8
9
10
Score after course
48
42
43
34
50
30
43
38
41
3
Score before course
31
34
18
30
44
28
34
33
27
32
Is there enough evidence to infer at the 5% significance level that the reading scores have improved?
27. Ten functionally illiterate adults were given an experimental one-week crash course in reading. Each
of the 10 was given a reading test prior to the course and another test after the course. The results are
shown below.
Adult
1
2
3
4
5
6
7
8
9
10
Score after course
48
42
43
34
50
30
43
38
41
3
Score before course
31
34
18
30
44
28
34
33
27
32
a. Estimate the mean improvement with 95% confidence.
b. Briefly describe what the interval estimate in part a. tells you.
28. Because of the rising costs of industrial accidents, many chemical, mining and manufacturing firms
have instituted safety courses. Employees are encouraged to take these courses, which are designed to
heighten safety awareness. A company is trying to decide which one of two courses to institute. To
help make a decision, eight employees take course 1 and another eight take course 2. Each employee
takes a test, which is graded out of a possible 25. The safety test results are shown below.
14
21
17
14
17
19
20
16
20
18
22
15
23
21
19
15
Assume that the scores are normally distributed. Does the data provide sufficient evidence at the 5%
level of significance to infer that the marks from course 1 are lower than those from course 2?
29. A political poll taken immediately prior to a state election reveals that 158 out of 250 male voters and
105 out of 200 female voters intend to vote for the Independent candidate.
Can we infer at the 5% significance level that the proportions of male and female voters who intend to
vote for the Independent candidate differ?
30. A political poll taken immediately prior to a state election reveals that 158 out of 250 male voters and
105 out of 200 female voters intend to vote for the Independent candidate.
a. What is the p-value of the test?
b. Estimate with 95% confidence the difference between the proportions of male and female voters
who intend to vote for the Independent candidate.
c. Explain how to use the interval estimate in part b. to test the hypotheses.
31. Thirty-five employees who completed two years of tertiary education were asked to take a basic
mathematics test. The mean and standard deviation of their marks were 75.1 and 12.8, respectively. In
a random sample of 50 employees who only completed high school, the mean and standard deviation
of the test marks were 72.1 and 14.6, respectively.
Can we infer at the 10% significance level that a difference exists between the two groups?
32. Thirty-five employees who completed two years of tertiary education were asked to take a basic
mathematics test. The mean and standard deviation of their marks were 75.1 and 12.8, respectively. In
a random sample of 50 employees who only completed high school, the mean and standard deviation
of the test marks were 72.1 and 14.6, respectively.
a. Estimate with 90% confidence the difference in mean scores between the two groups of
employees.
b. Explain how to use the interval estimate in part a. to test the hypotheses.
33. Do government employees take longer tea breaks than private-sector workers? That is the question that
interested a management consultant. To examine the issue, he took a random sample of nine
government employees and another random sample of nine private-sector workers and measured the
amount of time (in minutes) they spent in tea breaks during the day. The results are listed below.
Government
employees
Private sector
workers
23
25
18
19
34
18
31
22
28
28
33
25
25
21
27
21
32
30
Do these data provide sufficient evidence at the 5% significance level to answer the consultant’s
question in the affirmative?
34. Do government employees take longer tea breaks than private-sector workers? That is the question that
interested a management consultant. To examine the issue, he took a random sample of nine
government employees and another random sample of nine private-sector workers and measured the
amount of time (in minutes) they spent in tea breaks during the day. The results are listed below.
Government
employees
Private sector
workers
23
25
18
19
34
18
31
22
28
28
33
25
25
21
27
21
32
30
Estimate with 95% confidence the difference in mean tea-break time between the two groups and
explain what the interval estimate tells you.
35. A quality control inspector keeps a tally sheet of the numbers of acceptable and unacceptable products
that come off two different production lines. The completed sheet is shown below.
Production line
Acceptable
products
Unacceptable
products
1
152
48
2
136
54
Can the inspector infer at the 5% significance level that production line 1 is doing a better job than
production line 2?
36. A quality control inspector keeps a tally sheet of the numbers of acceptable and unacceptable products
that come off two different production lines. The completed sheet is shown below.
Production line
Acceptable
products
Unacceptable
products
1
152
48
2
136
54
a. What is the p-value of the test?
b. Estimate with 95% confidence the difference in population proportions.
37. A politician has commissioned a survey of blue-collar and white-collar employees in her electorate.
The survey reveals that 286 out of 542 blue-collar workers intend to vote for her in the next election,
whereas 428 out of 955 white-collar workers intend to vote for her.
a. Can she infer at the 5% level of significance that the level of support differs between the two
groups of workers?
b. What is the p-value of the test? Explain how to use it to test the hypotheses.
c. Estimate with 95% confidence the difference in population proportions.
d. Briefly describe what the interval estimate in part c. tells you.
38. An industrial statistician wants to determine whether efforts to promote safety have been successful.
By checking the records of 250 employees, he finds that 30 of them have suffered either minor or
major injuries that year. A random sample of 400 employees taken in the previous year revealed that
80 had suffered some form of injury.
a. Can the statistician infer at the 5% significance level that efforts to promote safety have been
successful?
b. What is the p-value of the test?
c. Estimate with 95% confidence the difference in population proportions.
39. Motor vehicle insurance appraisers examine cars that have been involved in accidental collisions to
assess the cost of repairs. An insurance executive is concerned that different appraisers produce
significantly different assessments. In an experiment, 10 cars that had recently been involved in
accidents were shown to two appraisers. Each assessed the estimated repair costs. The results are
shown below.
Car
Appraiser 1
Appraiser 2
1
1650
1400
2
360
380
3
640
600
4
1010
920
5
890
930
6
750
650
7
440
410
8
1210
1080
9
520
480
10
690
770
Can the executive conclude at the 5% significance level that the appraisers differ in their assessments?
40. A marketing consultant is studying the perceptions of married couples concerning their weekly food
expenditures. He believes that the husband’s perception would be higher than the wife’s. To judge his
belief, he takes a random sample of 10 married couples and asks each spouse to estimate the family
food expenditure (in dollars) during the previous week. The data are shown below.
Couple
Husband
Wife
1
380
270
2
280
300
3
215
185
4
350
320
5
210
180
6
410
390
7
250
250
8
360
320
9
180
170
10
400
330
Can the consultant conclude at the 5% significance level that the husband’s estimate is higher than the
wife’s estimate?
41. A marketing consultant is studying the perceptions of married couples concerning their weekly food
expenditures. He believes that the husband’s perception would be higher than the wife’s. To judge his
belief, he takes a random sample of 10 married couples and asks each spouse to estimate the family
food expenditure (in dollars) during the previous week. The data are shown below.
Couple
Husband
Wife
1
380
270
2
280
300
3
215
185
4
350
320
5
210
180
6
410
390
7
250
250
8
360
320
9
180
170
10
400
330
a. Estimate with 95% confidence the population mean difference.
b. Briefly describe what the interval estimate in part a. tells you.
42. A politician regularly polls her electorate to gauge her level of support among voters. This month, 652
out of 1158 voters support her. Five months ago, 412 out of 982 voters supported her. At the 5%
significance level, can she infer that support has increased by at least 10 percentage points?
43. Do interstate drivers exceed the speed limit more frequently than local motorists? This vital question
was addressed by the Road Traffic Authority. A random sample of the speeds of 2500 randomly
selected cars was categorised according to whether the car was registered in the state or in some other
state, and whether or not the car was violating the speed limit. The data are shown below.
Local cars
Interstate cars
Speeding
521
328
Not speeding
1141
510
Do these data provide enough evidence to support the highway patrol’s claim at the 5% significance
level?
44. Do interstate drivers exceed the speed limit more frequently than local motorists? This vital question
was addressed by the Road Traffic Authority. A random sample of the speeds of 2500 randomly
selected cars was categorised according to whether the car was registered in the state or in some other
state, and whether or not the car was violating the speed limit. The data are shown below.
Local cars
Interstate cars
Speeding
521
328
Not speeding
1141
510
a. Estimate with 95% confidence the difference in population proportions.
b. Briefly describe what the interval estimate in part a. tells you.
45. The managing director of a breakfast cereal manufacturer believes that families in which both spouses
work are much more likely to be consumers of his product than those with only one working spouse.
To prove his point, he commissions a survey of 300 families in which both spouses work and 300
families with only one working spouse. Each family is asked whether the company’s cereal is eaten for
breakfast. The results are shown below.
Two spouses
working
One spouse working
Eat cereal
114
87
Don’t eat cereal
186
213
Do these data provide enough evidence at the 1% significance level to infer that the proportion of
families with two working spouses who eat the cereal is at least 5% larger than the proportion of
families with one working spouse who eats the cereal?
46. The managing director of a breakfast cereal manufacturer believes that families in which both spouses
work are much more likely to be consumers of his product than those with only one working spouse.
To prove his point, he commissions a survey of 300 families in which both spouses work and 300
families with only one working spouse. Each family is asked whether the company’s cereal is eaten for
breakfast. The results are shown below.
Two spouses
working
One spouse working
Eat cereal
114
87
Don’t eat cereal
186
213
a. What is the p-value of the test?
b. Estimate with 99% confidence the difference in population proportions.
47. A psychologist has performed the following experiment. For each of 10 sets of identical twins who
were born 30 years ago, she recorded their annual incomes according to which twin was born first. The
results (in $000) are shown below.
Twin set
First born
Second born
1
32
44
2
36
43
3
21
28
4
30
39
5
49
51
6
27
25
7
39
32
8
38
42
9
56
64
10
44
44
Can she infer at the 5% significance level that there is a difference in income between the twins?
48. A management consultant wants to compare the incomes of graduates of MBA programs with those of
graduates with Bachelor’s degrees. In a random sample of the incomes of 20 people taken five years
after they received their MBAs, the consultant found the mean salary and the standard deviation to be
$45 300 and $9600, respectively. A random sample of the incomes of 25 people taken five years after
they received their Bachelor’s degrees yielded a mean salary of $43 600 with a standard deviation of
$12 300.
a. Can we infer at the 5% level of significance that the population means differ?
b. Estimate with 95% confidence the difference in mean salaries between MBA and Bachelor degree
graduates.
49. The marketing manager of a pharmaceutical company believes that more girls than boys use its acne
medicine. In a recent survey, 2500 teenagers were asked whether or not they use that particular
product. The responses, categorised by sex, are summarised below.
Use acne medicine
Don’t use acne medicine
Female
540
810
Male
391
759
a. Do these data provide enough evidence at the 10% significance level to support the manager’s
claim?
b. Estimate with 90% confidence the difference in the proportions of male and female users of the
acne medicine.
c. Describe what the interval estimate in part b. tells you.