3. A statistician kept track of the weight losses of ten people who were assigned diet A and the weight
losses of another ten people who were assigned diet B. These results are shown in the following table.
Weight losses
Diet A
Diet B
6
7
8
9
5
12
7
8
9
11
4
9
6
8
8
10
9
7
8
9
Do these data provide sufficient evidence at the 5% significance level to conclude that the mean
weight loss with diet A more than 6 kg? (Assume that the weight losses are normally distributed.)
4. A statistician kept track of the weight losses of ten people who were assigned diet A and the weight
losses of another ten people who were assigned diet B. These results are shown in the following table.
Weight losses
Diet A
Diet B
6
7
8
9
5
12
7
8
9
11
4
9
6
8
8
10
9
7
8
9
Do these data provide sufficient evidence at the 10% significance level to conclude that the mean
weight loss with diet B is less than 10 kg? (Assume that the weight losses are normally distributed.)
5. A statistician kept track of the weight losses of ten people who were assigned diet A and the weight
losses of another ten people who were assigned diet B. These results are shown in the following table.
Weight losses
Diet A
Diet B
6
7
8
9
5
12
7
8
9
11
4
9
6
8
8
10
9
7
8
9
Estimate with 95% confidence the difference in mean weight loss between diets A and B. (Assume
that the weight losses are normally distributed.)
6. A statistician kept track of the weight losses of ten people who were assigned diet A and the weight
losses of another ten people who were assigned diet B. These results are shown in the following table.
Weight losses
Diet A
Diet B
6
7
8
9
5
12
7
8
9
11
4
9
6
8
8
10
9
7
8
9
Estimate with 90% confidence the mean weight loss with diet A. (Assume that the weight losses are
normally distributed.)
7. A statistician kept track of the weight losses of ten people who were assigned diet A and the weight
losses of another ten people who were assigned diet B. These results are shown in the following table.
Weight losses
Diet A
Diet B
6
7
8
9
5
12
7
8
9
11
4
9
6
8
8
10
9
7
8
9
If we assume that the weight losses are not normally distributed, can we conclude at the 2.5%
significance level that diet B is more effective than diet A?
8. Most perishable foods sold in supermarkets have labels indicating the date by which the food is no
longer considered at its best. The period of time during which the food is considered at its best (called
the shelf-life) depends to some extent on the preservatives used. A research scientist is working on the
development of a new preservative that is designed to extend the shelf-life of a variety of foods. In an
experiment with eight different types of food, some of each type were treated with the currently used
preservative (preservative ABC), and some of each type were treated with the new experimental
preservative (preservative XYZ). The shelf-life (in days) for each was measured, with the results
shown in the following table.
Shelf life
Food type
Preservative
ABC
Preservative
XYZ
1
27
32
2
14
16
3
53
52
4
19
23
5
22
23
6
41
46
7
29
33
8
12
17
If we assume that the data are normally distributed, is there sufficient evidence at the 5% significance
level to conclude that preservative XYZ is superior?
9. Most perishable foods sold in supermarkets have labels indicating the date by which the food is no
longer considered at its best. The period of time during which the food is considered at its best (called
the shelf-life) depends to some extent on the preservatives used. A research scientist is working on the
development of a new preservative that is designed to extend the shelf-life of a variety of foods. In an
experiment with eight different types of food, some of each type were treated with the currently used
preservative (preservative ABC), and some of each type were treated with the new experimental
preservative (preservative XYZ). The shelf-life (in days) for each was measured, with the results
shown in the following table.
Shelf life
Food type
Preservative
ABC
Preservative
XYZ
1
27
32
2
14
16
3
53
52
4
19
23
5
22
23
6
41
46
7
29
33
8
12
17
Estimate with 99% confidence the mean difference in shelf-life between the two preservatives.
10. Most perishable foods sold in supermarkets have labels indicating the date by which the food is no
longer considered at its best. The period of time during which the food is considered at its best (called
the shelf-life) depends to some extent on the preservatives used. A research scientist is working on the
development of a new preservative that is designed to extend the shelf-life of a variety of foods. In an
experiment with eight different types of food, some of each type were treated with the currently used
preservative (preservative ABC), and some of each type were treated with the new experimental
preservative (preservative XYZ). The shelf-life (in days) for each was measured, with the results
shown in the following table.
Shelf life
Food type
Preservative
ABC
Preservative
XYZ
1
27
32
2
14
16
3
53
52
4
19
23
5
22
23
6
41
46
7
29
33
8
12
17
If we assume that the data are not normally distributed, is there sufficient evidence at the 5%
significance level to conclude that preservative XYZ is superior?
11. A study designed to analyse the factors involved in heart attacks was undertaken. A random sample of
75 60-year-old men was drawn, of whom 25 had not suffered a heart attack (Group 1), 25 had suffered
a minor heart attack (Group 2), and the remaining 25 had suffered a major heart attack (Group 3). Each
was asked how many hours of exercise they usually engage in weekly and whether they smoke, and, if
they do, whether they are moderate or heavy smokers. On the basis of a questionnaire, each is assigned
a stress score on a five-point basis, measuring how stressful they find their jobs. Question 1 deals with
the amount of weekly exercise. Question 2 deals with smoking. The responses are NS = nonsmoker,
MS = moderate smoker, and HS = heavy smoker. Question 3 deals with stress levels. The responses
range from 1 (no stress) to 5 (heavy stress). The results are summarised in the following table. It has
been determined that the amount of exercise is normally distributed.
Group 1
Group 2
Group 3
No heart attack
Minor heart attack
Major heart attack
Question 1: Mean and
=3.2
=2.3
=1.1
standard deviation
=0.5
=0.4
=0.4
Question 2:
Frequencies
NS: 15
NS: 11
NS: 7
MS: 7
MS: 8
MS: 5
HS: 3
HS: 6
HS: 13
Question 3:
Frequencies
1: 8
1: 4
1: 2
2: 6
2: 5
2: 3
3: 4
3: 6
3: 6
4: 4
4: 5
4: 7
5: 3
5: 5
5: 7
Can we conclude at the 5% significance level that there are differences in the amount of exercise
among the three groups of men?
12. A study designed to analyse the factors involved in heart attacks was undertaken. A random sample of
75 60-year-old men was drawn, of whom 25 had not suffered a heart attack (Group 1), 25 had suffered
a minor heart attack (Group 2), and the remaining 25 had suffered a major heart attack (Group 3). Each
was asked how many hours of exercise they usually engage in weekly and whether they smoke, and, if
they do, whether they are moderate or heavy smokers. On the basis of a questionnaire, each is assigned
a stress score on a five-point basis, measuring how stressful they find their jobs. Question 1 deals with
the amount of weekly exercise. Question 2 deals with smoking. The responses are NS = nonsmoker,
MS = moderate smoker, and HS = heavy smoker. Question 3 deals with stress levels. The responses
range from 1 (no stress) to 5 (heavy stress). The results are summarised in the following table. It has
been determined that the amount of exercise is normally distributed.
Group 1
Group 2
Group 3
No heart attack
Minor heart attack
Major heart attack
Question 1: Mean and
=3.2
=2.3
=1.1
standard deviation
=0.5
=0.4
=0.4
Question 2:
Frequencies
NS: 15
NS: 11
NS: 7
MS: 7
MS: 8
MS: 5
HS: 3
HS: 6
HS: 13
Question 3:
Frequencies
1: 8
1: 4
1: 2
2: 6
2: 5
2: 3
3: 4
3: 6
3: 6
4: 4
4: 5
4: 7
5: 3
5: 5
5: 7
Can we conclude at the 10% significance level that those who did not suffer a heart attack exercise
more than those who suffered a major heart attack?
13. A study designed to analyse the factors involved in heart attacks was undertaken. A random sample of
75 60-year-old men was drawn, of whom 25 had not suffered a heart attack (Group 1), 25 had suffered
a minor heart attack (Group 2), and the remaining 25 had suffered a major heart attack (Group 3). Each
was asked how many hours of exercise they usually engage in weekly and whether they smoke, and, if
they do, whether they are moderate or heavy smokers. On the basis of a questionnaire, each is assigned
a stress score on a five-point basis, measuring how stressful they find their jobs. Question 1 deals with
the amount of weekly exercise. Question 2 deals with smoking. The responses are NS = nonsmoker,
MS = moderate smoker, and HS = heavy smoker. Question 3 deals with stress levels. The responses
range from 1 (no stress) to 5 (heavy stress). The results are summarised in the following table. It has
been determined that the amount of exercise is normally distributed.
Group 1
Group 2
Group 3
No heart attack
Minor heart attack
Major heart attack
Question 1: Mean and
=3.2
=2.3
=1.1
standard deviation
=0.5
=0.4
=0.4
Question 2:
Frequencies
NS: 15
NS: 11
NS: 7
MS: 7
MS: 8
MS: 5
HS: 3
HS: 6
HS: 13
Question 3:
Frequencies
1: 8
1: 4
1: 2
2: 6
2: 5
2: 3
3: 4
3: 6
3: 6
4: 4
4: 5
4: 7
5: 3
5: 5
5: 7
Estimate with 90% confidence the difference between the mean exercise time of those who have not
had a heart attack and the mean exercise time of those who’ve had minor heart attacks.
14. A study designed to analyse the factors involved in heart attacks was undertaken. A random sample of
75 60-year-old men was drawn, of whom 25 had not suffered a heart attack (Group 1), 25 had suffered
a minor heart attack (Group 2), and the remaining 25 had suffered a major heart attack (Group 3). Each
was asked how many hours of exercise they usually engage in weekly and whether they smoke, and, if
they do, whether they are moderate or heavy smokers. On the basis of a questionnaire, each is assigned
a stress score on a five-point basis, measuring how stressful they find their jobs. Question 1 deals with
the amount of weekly exercise. Question 2 deals with smoking. The responses are NS = nonsmoker,
MS = moderate smoker, and HS = heavy smoker. Question 3 deals with stress levels. The responses
range from 1 (no stress) to 5 (heavy stress). The results are summarised in the following table. It has
been determined that the amount of exercise is normally distributed.
Group 1
Group 2
Group 3
No heart attack
Minor heart attack
Major heart attack
Question 1: Mean and
=3.2
=2.3
=1.1
standard deviation
=0.5
=0.4
=0.4
Question 2:
Frequencies
NS: 15
NS: 11
NS: 7
MS: 7
MS: 8
MS: 5
HS: 3
HS: 6
HS: 13
Question 3:
Frequencies
1: 8
1: 4
1: 2
2: 6
2: 5
2: 3
3: 4
3: 6
3: 6
4: 4
4: 5
4: 7
5: 3
5: 5
5: 7
Can we conclude at the 1% significance level that the mean exercise time for those who’ve had major
heart attacks is no more than 1.3 hours per week?
15. A study designed to analyse the factors involved in heart attacks was undertaken. A random sample of
75 60-year-old men was drawn, of whom 25 had not suffered a heart attack (Group 1), 25 had suffered
a minor heart attack (Group 2), and the remaining 25 had suffered a major heart attack (Group 3). Each
was asked how many hours of exercise they usually engage in weekly and whether they smoke, and, if
they do, whether they are moderate or heavy smokers. On the basis of a questionnaire, each is assigned
a stress score on a five-point basis, measuring how stressful they find their jobs. Question 1 deals with
the amount of weekly exercise. Question 2 deals with smoking. The responses are NS = nonsmoker,
MS = moderate smoker, and HS = heavy smoker. Question 3 deals with stress levels. The responses
range from 1 (no stress) to 5 (heavy stress). The results are summarised in the following table. It has
been determined that the amount of exercise is normally distributed.
Group 1
Group 2
Group 3
No heart attack
Minor heart attack
Major heart attack
Question 1: Mean and
=3.2
=2.3
=1.1
standard deviation
=0.5
=0.4
=0.4
Question 2:
Frequencies
NS: 15
NS: 11
NS: 7
MS: 7
MS: 8
MS: 5
HS: 3
HS: 6
HS: 13
Question 3:
Frequencies
1: 8
1: 4
1: 2
2: 6
2: 5
2: 3
3: 4
3: 6
3: 6
4: 4
4: 5
4: 7
5: 3
5: 5
5: 7
Estimate with 99% confidence the mean exercise time among those who’ve had minor heart attacks.
16. A study designed to analyse the factors involved in heart attacks was undertaken. A random sample of
75 60-year-old men was drawn, of whom 25 had not suffered a heart attack (Group 1), 25 had suffered
a minor heart attack (Group 2), and the remaining 25 had suffered a major heart attack (Group 3). Each
was asked how many hours of exercise they usually engage in weekly and whether they smoke, and, if
they do, whether they are moderate or heavy smokers. On the basis of a questionnaire, each is assigned
a stress score on a five-point basis, measuring how stressful they find their jobs. Question 1 deals with
the amount of weekly exercise. Question 2 deals with smoking. The responses are NS = nonsmoker,
MS = moderate smoker, and HS = heavy smoker. Question 3 deals with stress levels. The responses
range from 1 (no stress) to 5 (heavy stress). The results are summarised in the following table. It has
been determined that the amount of exercise is normally distributed.
Group 1
Group 2
Group 3
No heart attack
Minor heart attack
Major heart attack
Question 1: Mean and
=3.2
=2.3
=1.1
standard deviation
=0.5
=0.4
=0.4
Question 2:
Frequencies
NS: 15
NS: 11
NS: 7
MS: 7
MS: 8
MS: 5
HS: 3
HS: 6
HS: 13
Question 3:
Frequencies
1: 8
1: 4
1: 2
2: 6
2: 5
2: 3
3: 4
3: 6
3: 6
4: 4
4: 5
4: 7
5: 3
5: 5
5: 7
Can we conclude at the 10% significance level that the amount of smoking differs among the three
groups of men?
17. A study designed to analyse the factors involved in heart attacks was undertaken. A random sample of
75 60-year-old men was drawn, of whom 25 had not suffered a heart attack (Group 1), 25 had suffered
a minor heart attack (Group 2), and the remaining 25 had suffered a major heart attack (Group 3). Each
was asked how many hours of exercise they usually engage in weekly and whether they smoke, and, if
they do, whether they are moderate or heavy smokers. On the basis of a questionnaire, each is assigned
a stress score on a five-point basis, measuring how stressful they find their jobs. Question 1 deals with
the amount of weekly exercise. Question 2 deals with smoking. The responses are NS = nonsmoker,
MS = moderate smoker, and HS = heavy smoker. Question 3 deals with stress levels. The responses
range from 1 (no stress) to 5 (heavy stress). The results are summarised in the following table. It has
been determined that the amount of exercise is normally distributed.
Group 1
Group 2
Group 3
No heart attack
Minor heart attack
Major heart attack
Question 1: Mean and
=3.2
=2.3
=1.1
standard deviation
=0.5
=0.4
=0.4
Question 2:
Frequencies
NS: 15
NS: 11
NS: 7
MS: 7
MS: 8
MS: 5
HS: 3
HS: 6
HS: 13
Question 3:
Frequencies
1: 8
1: 4
1: 2
2: 6
2: 5
2: 3
3: 4
3: 6
3: 6
4: 4
4: 5
4: 7
5: 3
5: 5
5: 7
Can we conclude at the 5% significance level that those who have suffered major heart attacks smoke
more than those who have not suffered any heart attacks?
18. A study designed to analyse the factors involved in heart attacks was undertaken. A random sample of
75 60-year-old men was drawn, of whom 25 had not suffered a heart attack (Group 1), 25 had suffered
a minor heart attack (Group 2), and the remaining 25 had suffered a major heart attack (Group 3). Each
was asked how many hours of exercise they usually engage in weekly and whether they smoke, and, if
they do, whether they are moderate or heavy smokers. On the basis of a questionnaire, each is assigned
a stress score on a five-point basis, measuring how stressful they find their jobs. Question 1 deals with
the amount of weekly exercise. Question 2 deals with smoking. The responses are NS = nonsmoker,
MS = moderate smoker, and HS = heavy smoker. Question 3 deals with stress levels. The responses
range from 1 (no stress) to 5 (heavy stress). The results are summarised in the following table. It has
been determined that the amount of exercise is normally distributed.
Group 1
Group 2
Group 3
No heart attack
Minor heart attack
Major heart attack
Question 1: Mean and
=3.2
=2.3
=1.1
standard deviation
=0.5
=0.4
=0.4
Question 2:
Frequencies
NS: 15
NS: 11
NS: 7
MS: 7
MS: 8
MS: 5
HS: 3
HS: 6
HS: 13
Question 3:
Frequencies
1: 8
1: 4
1: 2
2: 6
2: 5
2: 3
3: 4
3: 6
3: 6
4: 4
4: 5
4: 7
5: 3
5: 5
5: 7
a. Can we conclude at the 5% significance level that there are more nonsmokers in Group 1 than in
Group 2?
b. Find the p-value of the test.
19. A study designed to analyse the factors involved in heart attacks was undertaken. A random sample of
75 60-year-old men was drawn, of whom 25 had not suffered a heart attack (Group 1), 25 had suffered
a minor heart attack (Group 2), and the remaining 25 had suffered a major heart attack (Group 3). Each
was asked how many hours of exercise they usually engage in weekly and whether they smoke, and, if
they do, whether they are moderate or heavy smokers. On the basis of a questionnaire, each is assigned
a stress score on a five-point basis, measuring how stressful they find their jobs. Question 1 deals with
the amount of weekly exercise. Question 2 deals with smoking. The responses are NS = nonsmoker,
MS = moderate smoker, and HS = heavy smoker. Question 3 deals with stress levels. The responses
range from 1 (no stress) to 5 (heavy stress). The results are summarised in the following table. It has
been determined that the amount of exercise is normally distributed.
Group 1
Group 2
Group 3
No heart attack
Minor heart attack
Major heart attack
Question 1: Mean and
=3.2
=2.3
=1.1
standard deviation
=0.5
=0.4
=0.4
Question 2:
Frequencies
NS: 15
NS: 11
NS: 7
MS: 7
MS: 8
MS: 5
HS: 3
HS: 6
HS: 13
Question 3:
Frequencies
1: 8
1: 4
1: 2
2: 6
2: 5
2: 3
3: 4
3: 6
3: 6
4: 4
4: 5
4: 7
5: 3
5: 5
5: 7
Estimate with 99% confidence the difference in the proportion of nonsmokers between Groups 2 and
3.
20. A study designed to analyse the factors involved in heart attacks was undertaken. A random sample of
75 60-year-old men was drawn, of whom 25 had not suffered a heart attack (Group 1), 25 had suffered
a minor heart attack (Group 2), and the remaining 25 had suffered a major heart attack (Group 3). Each
was asked how many hours of exercise they usually engage in weekly and whether they smoke, and, if
they do, whether they are moderate or heavy smokers. On the basis of a questionnaire, each is assigned
a stress score on a five-point basis, measuring how stressful they find their jobs. Question 1 deals with
the amount of weekly exercise. Question 2 deals with smoking. The responses are NS = nonsmoker,
MS = moderate smoker, and HS = heavy smoker. Question 3 deals with stress levels. The responses
range from 1 (no stress) to 5 (heavy stress). The results are summarised in the following table. It has
been determined that the amount of exercise is normally distributed.
Group 1
Group 2
Group 3
No heart attack
Minor heart attack
Major heart attack
Question 1: Mean and
=3.2
=2.3
=1.1
standard deviation
=0.5
=0.4
=0.4
Question 2:
Frequencies
NS: 15
NS: 11
NS: 7
MS: 7
MS: 8
MS: 5
HS: 3
HS: 6
HS: 13
Question 3:
Frequencies
1: 8
1: 4
1: 2
2: 6
2: 5
2: 3
3: 4
3: 6
3: 6
4: 4
4: 5
4: 7
5: 3
5: 5
5: 7
a. Can we conclude at the 5% significance level that the proportion of smokers in Group 3 is at least
50%?
b. Find the p-value of the test.
21. A study designed to analyse the factors involved in heart attacks was undertaken. A random sample of
75 60-year-old men was drawn, of whom 25 had not suffered a heart attack (Group 1), 25 had suffered
a minor heart attack (Group 2), and the remaining 25 had suffered a major heart attack (Group 3). Each
was asked how many hours of exercise they usually engage in weekly and whether they smoke, and, if
they do, whether they are moderate or heavy smokers. On the basis of a questionnaire, each is assigned
a stress score on a five-point basis, measuring how stressful they find their jobs. Question 1 deals with
the amount of weekly exercise. Question 2 deals with smoking. The responses are NS = nonsmoker,
MS = moderate smoker, and HS = heavy smoker. Question 3 deals with stress levels. The responses
range from 1 (no stress) to 5 (heavy stress). The results are summarised in the following table. It has
been determined that the amount of exercise is normally distributed.
Group 1
Group 2
Group 3
No heart attack
Minor heart attack
Major heart attack
Question 1: Mean and
=3.2
=2.3
=1.1
standard deviation
=0.5
=0.4
=0.4
Question 2:
Frequencies
NS: 15
NS: 11
NS: 7
MS: 7
MS: 8
MS: 5
HS: 3
HS: 6
HS: 13
Question 3:
Frequencies
1: 8
1: 4
1: 2
2: 6
2: 5
2: 3
3: 4
3: 6
3: 6
4: 4
4: 5
4: 7
5: 3
5: 5
5: 7
Estimate with 99% confidence the proportion of smokers in Group 2.
22. A study designed to analyse the factors involved in heart attacks was undertaken. A random sample of
75 60-year-old men was drawn, of whom 25 had not suffered a heart attack (Group 1), 25 had suffered
a minor heart attack (Group 2), and the remaining 25 had suffered a major heart attack (Group 3). Each
was asked how many hours of exercise they usually engage in weekly and whether they smoke, and, if
they do, whether they are moderate or heavy smokers. On the basis of a questionnaire, each is assigned
a stress score on a five-point basis, measuring how stressful they find their jobs. Question 1 deals with
the amount of weekly exercise. Question 2 deals with smoking. The responses are NS = nonsmoker,
MS = moderate smoker, and HS = heavy smoker. Question 3 deals with stress levels. The responses
range from 1 (no stress) to 5 (heavy stress). The results are summarised in the following table. It has
been determined that the amount of exercise is normally distributed.
Group 1
Group 2
Group 3
No heart attack
Minor heart attack
Major heart attack
Question 1: Mean and
=3.2
=2.3
=1.1
standard deviation
=0.5
=0.4
=0.4
Question 2:
Frequencies
NS: 15
NS: 11
NS: 7
MS: 7
MS: 8
MS: 5
HS: 3
HS: 6
HS: 13
Question 3:
Frequencies
1: 8
1: 4
1: 2
2: 6
2: 5
2: 3
3: 4
3: 6
3: 6
4: 4
4: 5
4: 7
5: 3
5: 5
5: 7
Can we conclude at the 10% significance level that there are differences in stress levels among the
three Groups of men?
23. A study designed to analyse the factors involved in heart attacks was undertaken. A random sample of
75 60-year-old men was drawn, of whom 25 had not suffered a heart attack (Group 1), 25 had suffered
a minor heart attack (Group 2), and the remaining 25 had suffered a major heart attack (Group 3). Each
was asked how many hours of exercise they usually engage in weekly and whether they smoke, and, if
they do, whether they are moderate or heavy smokers. On the basis of a questionnaire, each is assigned
a stress score on a five-point basis, measuring how stressful they find their jobs. Question 1 deals with
the amount of weekly exercise. Question 2 deals with smoking. The responses are NS = nonsmoker,
MS = moderate smoker, and HS = heavy smoker. Question 3 deals with stress levels. The responses
range from 1 (no stress) to 5 (heavy stress). The results are summarised in the following table. It has
been determined that the amount of exercise is normally distributed.