State the null hypothesis.

Question

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Answer 1

Question

Chapter 16, Problem 14E

a.

To determine

State the null hypothesis.

a.

Expert Solution

Explanation of Solution

In this context, the sample size n is 14.

The test hypotheses are given below:

Null hypothesis:

H0: The production is same using the old work environment and new work environment.

b.

To determine

Decide the alternative hypothesis.

b.

Expert Solution

Explanation of Solution

The answers will vary. One of the possible answers is given below:

Here, it is assumed that the production has been increased in the new work environment.

Alternative hypothesis:

H1: The production using the new work environment has increased than old work environment.

c.

To determine

Decide the level of significance.

c.

Expert Solution

Explanation of Solution

The answers will vary. One of the possible answers is given below:

In general, the level of significance may decide upon the interest of the researcher. Assume that the level of significance is α=0.05.

d.

To determine

Provide the decision rule.

d.

Expert Solution

Explanation of Solution

The table represents the computations of the test statistic:

Employee	Difference = {Old−New}	Absolute Difference	Rank	Signed Rank
Employee	Difference = {Old−New}	Absolute Difference	Rank	R⁺	R^-
1	−10(=23−33)	10	13		−
2	0(=26−26)	-		-	-
3	−6(=24−30)	6	9		−
4	−8(=17−25)	8	11		−
5	1(=20−19)	1	1	+
6	2(=24−22)	2	4	+
7	1(=30−29)	1	1	+
8	−4(=21−25)	4	7		−
9	3 (=25−22)	3	6	+
10	-2 (=21−23)	2	4		−
11	-1 (=16−17)	1	1		−
12	5 (=20−15)	5	8	+
13	8(=17−9)	8	11	+
14	−7 (=23−30)	7	10		−

Decision rule:

If T≤Tα, reject the null hypothesis.
Otherwise, fail to reject the null hypothesis.

In this context, the alternative is two-tailed test and the total number of ranks is 13.

From Appendix B, Table B.8 Wilcoxon T values:

Procedure:

1. In the Wilcoxon T values, locate n as 13.
2. Locate the value of 0.05 in α.
3. Locate the intersection value of the row and column. This gives the critical value.

The critical value for 0.05 the significance level is 21.

Decision rule:

If T≤21, reject the null hypothesis.
Otherwise, fail to reject the null hypothesis.

e.

To determine

Make the necessary conclusions regarding the null hypothesis.

e.

Expert Solution

Answer to Problem 14E

The null hypothesis is not rejected.

Explanation of Solution

The sum of positive ranks is denoted as R⁺, and the sum of negative ranks is denoted as R^-.

Here,

R+=1+4+1+6+8+11=31

R−={13+9+11+7+4+1+10}=55

For the Wilcoxon signed-rank test, the test statistic will be obtained as follows:

T=Min(R+,R−)

In this context, the test statistic for sample size 13 is Min(31,55). Therefore, the test statistic is 31.

Conclusion:

Here, the test statistic is greater than the critical value.

Therefore, by the decision rule, fail to reject the null hypothesis.

Therefore, there is no enough evidence that the production using the new work environment has increased than the old.

f.

To determine

State the assumption that has been assumed about the distribution of difference.

f.

Expert Solution

Explanation of Solution

In this context, none of the assumption is required for the distribution of difference.

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Answer 2

Question

Chapter 16, Problem 14E

a.

To determine

State the null hypothesis.

a.

Expert Solution

Explanation of Solution

In this context, the sample size n is 14.

The test hypotheses are given below:

Null hypothesis:

H0: The production is same using the old work environment and new work environment.

b.

To determine

Decide the alternative hypothesis.

b.

Expert Solution

Explanation of Solution

The answers will vary. One of the possible answers is given below:

Here, it is assumed that the production has been increased in the new work environment.

Alternative hypothesis:

H1: The production using the new work environment has increased than old work environment.

c.

To determine

Decide the level of significance.

c.

Expert Solution

Explanation of Solution

The answers will vary. One of the possible answers is given below:

In general, the level of significance may decide upon the interest of the researcher. Assume that the level of significance is α=0.05.

d.

To determine

Provide the decision rule.

d.

Expert Solution

Explanation of Solution

The table represents the computations of the test statistic:

Employee	Difference = {Old−New}	Absolute Difference	Rank	Signed Rank
Employee	Difference = {Old−New}	Absolute Difference	Rank	R⁺	R^-
1	−10(=23−33)	10	13		−
2	0(=26−26)	-		-	-
3	−6(=24−30)	6	9		−
4	−8(=17−25)	8	11		−
5	1(=20−19)	1	1	+
6	2(=24−22)	2	4	+
7	1(=30−29)	1	1	+
8	−4(=21−25)	4	7		−
9	3 (=25−22)	3	6	+
10	-2 (=21−23)	2	4		−
11	-1 (=16−17)	1	1		−
12	5 (=20−15)	5	8	+
13	8(=17−9)	8	11	+
14	−7 (=23−30)	7	10		−

Decision rule:

If T≤Tα, reject the null hypothesis.
Otherwise, fail to reject the null hypothesis.

In this context, the alternative is two-tailed test and the total number of ranks is 13.

From Appendix B, Table B.8 Wilcoxon T values:

Procedure:

1. In the Wilcoxon T values, locate n as 13.
2. Locate the value of 0.05 in α.
3. Locate the intersection value of the row and column. This gives the critical value.

The critical value for 0.05 the significance level is 21.

Decision rule:

If T≤21, reject the null hypothesis.
Otherwise, fail to reject the null hypothesis.

e.

To determine

Make the necessary conclusions regarding the null hypothesis.

e.

Expert Solution

Answer to Problem 14E

The null hypothesis is not rejected.

Explanation of Solution

The sum of positive ranks is denoted as R⁺, and the sum of negative ranks is denoted as R^-.

Here,

R+=1+4+1+6+8+11=31

R−={13+9+11+7+4+1+10}=55

For the Wilcoxon signed-rank test, the test statistic will be obtained as follows:

T=Min(R+,R−)

In this context, the test statistic for sample size 13 is Min(31,55). Therefore, the test statistic is 31.

Conclusion:

Here, the test statistic is greater than the critical value.

Therefore, by the decision rule, fail to reject the null hypothesis.

Therefore, there is no enough evidence that the production using the new work environment has increased than the old.

f.

To determine

State the assumption that has been assumed about the distribution of difference.

f.

Expert Solution

Explanation of Solution

In this context, none of the assumption is required for the distribution of difference.

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Answer 3

Question

Chapter 16, Problem 14E

a.

To determine

State the null hypothesis.

a.

Expert Solution

Explanation of Solution

In this context, the sample size n is 14.

The test hypotheses are given below:

Null hypothesis:

H0: The production is same using the old work environment and new work environment.

b.

To determine

Decide the alternative hypothesis.

b.

Expert Solution

Explanation of Solution

The answers will vary. One of the possible answers is given below:

Here, it is assumed that the production has been increased in the new work environment.

Alternative hypothesis:

H1: The production using the new work environment has increased than old work environment.

c.

To determine

Decide the level of significance.

c.

Expert Solution

Explanation of Solution

The answers will vary. One of the possible answers is given below:

In general, the level of significance may decide upon the interest of the researcher. Assume that the level of significance is α=0.05.

d.

To determine

Provide the decision rule.

d.

Expert Solution

Explanation of Solution

The table represents the computations of the test statistic:

Employee	Difference = {Old−New}	Absolute Difference	Rank	Signed Rank
Employee	Difference = {Old−New}	Absolute Difference	Rank	R⁺	R^-
1	−10(=23−33)	10	13		−
2	0(=26−26)	-		-	-
3	−6(=24−30)	6	9		−
4	−8(=17−25)	8	11		−
5	1(=20−19)	1	1	+
6	2(=24−22)	2	4	+
7	1(=30−29)	1	1	+
8	−4(=21−25)	4	7		−
9	3 (=25−22)	3	6	+
10	-2 (=21−23)	2	4		−
11	-1 (=16−17)	1	1		−
12	5 (=20−15)	5	8	+
13	8(=17−9)	8	11	+
14	−7 (=23−30)	7	10		−

Decision rule:

If T≤Tα, reject the null hypothesis.
Otherwise, fail to reject the null hypothesis.

In this context, the alternative is two-tailed test and the total number of ranks is 13.

From Appendix B, Table B.8 Wilcoxon T values:

Procedure:

1. In the Wilcoxon T values, locate n as 13.
2. Locate the value of 0.05 in α.
3. Locate the intersection value of the row and column. This gives the critical value.

The critical value for 0.05 the significance level is 21.

Decision rule:

If T≤21, reject the null hypothesis.
Otherwise, fail to reject the null hypothesis.

e.

To determine

Make the necessary conclusions regarding the null hypothesis.

e.

Expert Solution

Answer to Problem 14E

The null hypothesis is not rejected.

Explanation of Solution

The sum of positive ranks is denoted as R⁺, and the sum of negative ranks is denoted as R^-.

Here,

R+=1+4+1+6+8+11=31

R−={13+9+11+7+4+1+10}=55

For the Wilcoxon signed-rank test, the test statistic will be obtained as follows:

T=Min(R+,R−)

In this context, the test statistic for sample size 13 is Min(31,55). Therefore, the test statistic is 31.

Conclusion:

Here, the test statistic is greater than the critical value.

Therefore, by the decision rule, fail to reject the null hypothesis.

Therefore, there is no enough evidence that the production using the new work environment has increased than the old.

f.

To determine

State the assumption that has been assumed about the distribution of difference.

f.

Expert Solution

Explanation of Solution

In this context, none of the assumption is required for the distribution of difference.

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Answer 4

Question

Chapter 16, Problem 14E

a.

To determine

State the null hypothesis.

a.

Expert Solution

Explanation of Solution

In this context, the sample size n is 14.

The test hypotheses are given below:

Null hypothesis:

H0: The production is same using the old work environment and new work environment.

b.

To determine

Decide the alternative hypothesis.

b.

Expert Solution

Explanation of Solution

The answers will vary. One of the possible answers is given below:

Here, it is assumed that the production has been increased in the new work environment.

Alternative hypothesis:

H1: The production using the new work environment has increased than old work environment.

c.

To determine

Decide the level of significance.

c.

Expert Solution

Explanation of Solution

The answers will vary. One of the possible answers is given below:

In general, the level of significance may decide upon the interest of the researcher. Assume that the level of significance is α=0.05.

d.

To determine

Provide the decision rule.

d.

Expert Solution

Explanation of Solution

The table represents the computations of the test statistic:

Employee	Difference = {Old−New}	Absolute Difference	Rank	Signed Rank
Employee	Difference = {Old−New}	Absolute Difference	Rank	R⁺	R^-
1	−10(=23−33)	10	13		−
2	0(=26−26)	-		-	-
3	−6(=24−30)	6	9		−
4	−8(=17−25)	8	11		−
5	1(=20−19)	1	1	+
6	2(=24−22)	2	4	+
7	1(=30−29)	1	1	+
8	−4(=21−25)	4	7		−
9	3 (=25−22)	3	6	+
10	-2 (=21−23)	2	4		−
11	-1 (=16−17)	1	1		−
12	5 (=20−15)	5	8	+
13	8(=17−9)	8	11	+
14	−7 (=23−30)	7	10		−

Decision rule:

If T≤Tα, reject the null hypothesis.
Otherwise, fail to reject the null hypothesis.

In this context, the alternative is two-tailed test and the total number of ranks is 13.

From Appendix B, Table B.8 Wilcoxon T values:

Procedure:

1. In the Wilcoxon T values, locate n as 13.
2. Locate the value of 0.05 in α.
3. Locate the intersection value of the row and column. This gives the critical value.

The critical value for 0.05 the significance level is 21.

Decision rule:

If T≤21, reject the null hypothesis.
Otherwise, fail to reject the null hypothesis.

e.

To determine

Make the necessary conclusions regarding the null hypothesis.

e.

Expert Solution

Answer to Problem 14E

The null hypothesis is not rejected.

Explanation of Solution

The sum of positive ranks is denoted as R⁺, and the sum of negative ranks is denoted as R^-.

Here,

R+=1+4+1+6+8+11=31

R−={13+9+11+7+4+1+10}=55

For the Wilcoxon signed-rank test, the test statistic will be obtained as follows:

T=Min(R+,R−)

In this context, the test statistic for sample size 13 is Min(31,55). Therefore, the test statistic is 31.

Conclusion:

Here, the test statistic is greater than the critical value.

Therefore, by the decision rule, fail to reject the null hypothesis.

Therefore, there is no enough evidence that the production using the new work environment has increased than the old.

f.

To determine

State the assumption that has been assumed about the distribution of difference.

f.

Expert Solution

Explanation of Solution

In this context, none of the assumption is required for the distribution of difference.

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Answer 5

Chapter 16, Problem 14E

a.

To determine

State the null hypothesis.

a.

Expert Solution

Explanation of Solution

In this context, the sample size n is 14.

The test hypotheses are given below:

Null hypothesis:

H0: The production is same using the old work environment and new work environment.

b.

To determine

Decide the alternative hypothesis.

b.

Expert Solution

Explanation of Solution

The answers will vary. One of the possible answers is given below:

Here, it is assumed that the production has been increased in the new work environment.

Alternative hypothesis:

H1: The production using the new work environment has increased than old work environment.

c.

To determine

Decide the level of significance.

c.

Expert Solution

Explanation of Solution

The answers will vary. One of the possible answers is given below:

In general, the level of significance may decide upon the interest of the researcher. Assume that the level of significance is α=0.05.

d.

To determine

Provide the decision rule.

d.

Expert Solution

Explanation of Solution

The table represents the computations of the test statistic:

Employee	Difference = {Old−New}	Absolute Difference	Rank	Signed Rank
Employee	Difference = {Old−New}	Absolute Difference	Rank	R⁺	R^-
1	−10(=23−33)	10	13		−
2	0(=26−26)	-		-	-
3	−6(=24−30)	6	9		−
4	−8(=17−25)	8	11		−
5	1(=20−19)	1	1	+
6	2(=24−22)	2	4	+
7	1(=30−29)	1	1	+
8	−4(=21−25)	4	7		−
9	3 (=25−22)	3	6	+
10	-2 (=21−23)	2	4		−
11	-1 (=16−17)	1	1		−
12	5 (=20−15)	5	8	+
13	8(=17−9)	8	11	+
14	−7 (=23−30)	7	10		−

Decision rule:

If T≤Tα, reject the null hypothesis.
Otherwise, fail to reject the null hypothesis.

In this context, the alternative is two-tailed test and the total number of ranks is 13.

From Appendix B, Table B.8 Wilcoxon T values:

Procedure:

1. In the Wilcoxon T values, locate n as 13.
2. Locate the value of 0.05 in α.
3. Locate the intersection value of the row and column. This gives the critical value.

The critical value for 0.05 the significance level is 21.

Decision rule:

If T≤21, reject the null hypothesis.
Otherwise, fail to reject the null hypothesis.

e.

To determine

Make the necessary conclusions regarding the null hypothesis.

e.

Expert Solution

Answer to Problem 14E

The null hypothesis is not rejected.

Explanation of Solution

The sum of positive ranks is denoted as R⁺, and the sum of negative ranks is denoted as R^-.

Here,

R+=1+4+1+6+8+11=31

R−={13+9+11+7+4+1+10}=55

For the Wilcoxon signed-rank test, the test statistic will be obtained as follows:

T=Min(R+,R−)

In this context, the test statistic for sample size 13 is Min(31,55). Therefore, the test statistic is 31.

Conclusion:

Here, the test statistic is greater than the critical value.

Therefore, by the decision rule, fail to reject the null hypothesis.

Therefore, there is no enough evidence that the production using the new work environment has increased than the old.

f.

To determine

State the assumption that has been assumed about the distribution of difference.

f.

Expert Solution

Explanation of Solution

In this context, none of the assumption is required for the distribution of difference.

Answer 6

Chapter 16, Problem 14E

a.

To determine

State the null hypothesis.

a.

Expert Solution

Explanation of Solution

In this context, the sample size n is 14.

The test hypotheses are given below:

Null hypothesis:

H0: The production is same using the old work environment and new work environment.

Answer 7

Chapter 16, Problem 14E

a.

To determine

State the null hypothesis.

Answer 8

a.

Expert Solution

Explanation of Solution

In this context, the sample size n is 14.

The test hypotheses are given below:

Null hypothesis:

H0: The production is same using the old work environment and new work environment.

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

b.

To determine

Decide the alternative hypothesis.

b.

Expert Solution

Explanation of Solution

The answers will vary. One of the possible answers is given below:

Here, it is assumed that the production has been increased in the new work environment.

Alternative hypothesis:

H1: The production using the new work environment has increased than old work environment.

Answer 13

b.

To determine

Decide the alternative hypothesis.

Answer 14

b.

Expert Solution

Explanation of Solution

The answers will vary. One of the possible answers is given below:

Here, it is assumed that the production has been increased in the new work environment.

Alternative hypothesis:

H1: The production using the new work environment has increased than old work environment.

Answer 15

b.

Expert Solution

Answer 16

b.

Expert Solution

Answer 17

Expert Solution

Answer 18

c.

To determine

Decide the level of significance.

c.

Expert Solution

Explanation of Solution

The answers will vary. One of the possible answers is given below:

In general, the level of significance may decide upon the interest of the researcher. Assume that the level of significance is α=0.05.

Answer 19

c.

To determine

Decide the level of significance.

Answer 20

c.

Expert Solution

Explanation of Solution

The answers will vary. One of the possible answers is given below:

In general, the level of significance may decide upon the interest of the researcher. Assume that the level of significance is α=0.05.

Answer 21

c.

Expert Solution

Answer 22

c.

Expert Solution

Answer 23

Expert Solution

Answer 24

d.

To determine

Provide the decision rule.

d.

Expert Solution

Explanation of Solution

The table represents the computations of the test statistic:

Employee	Difference = {Old−New}	Absolute Difference	Rank	Signed Rank
Employee	Difference = {Old−New}	Absolute Difference	Rank	R⁺	R^-
1	−10(=23−33)	10	13		−
2	0(=26−26)	-		-	-
3	−6(=24−30)	6	9		−
4	−8(=17−25)	8	11		−
5	1(=20−19)	1	1	+
6	2(=24−22)	2	4	+
7	1(=30−29)	1	1	+
8	−4(=21−25)	4	7		−
9	3 (=25−22)	3	6	+
10	-2 (=21−23)	2	4		−
11	-1 (=16−17)	1	1		−
12	5 (=20−15)	5	8	+
13	8(=17−9)	8	11	+
14	−7 (=23−30)	7	10		−

Decision rule:

If T≤Tα, reject the null hypothesis.
Otherwise, fail to reject the null hypothesis.

In this context, the alternative is two-tailed test and the total number of ranks is 13.

From Appendix B, Table B.8 Wilcoxon T values:

Procedure:

1. In the Wilcoxon T values, locate n as 13.
2. Locate the value of 0.05 in α.
3. Locate the intersection value of the row and column. This gives the critical value.

The critical value for 0.05 the significance level is 21.

Decision rule:

If T≤21, reject the null hypothesis.
Otherwise, fail to reject the null hypothesis.

Answer 25

d.

To determine

Provide the decision rule.

Answer 26

d.

Expert Solution

Explanation of Solution

The table represents the computations of the test statistic:

Employee	Difference = {Old−New}	Absolute Difference	Rank	Signed Rank
Employee	Difference = {Old−New}	Absolute Difference	Rank	R⁺	R^-
1	−10(=23−33)	10	13		−
2	0(=26−26)	-		-	-
3	−6(=24−30)	6	9		−
4	−8(=17−25)	8	11		−
5	1(=20−19)	1	1	+
6	2(=24−22)	2	4	+
7	1(=30−29)	1	1	+
8	−4(=21−25)	4	7		−
9	3 (=25−22)	3	6	+
10	-2 (=21−23)	2	4		−
11	-1 (=16−17)	1	1		−
12	5 (=20−15)	5	8	+
13	8(=17−9)	8	11	+
14	−7 (=23−30)	7	10		−

Decision rule:

If T≤Tα, reject the null hypothesis.
Otherwise, fail to reject the null hypothesis.

In this context, the alternative is two-tailed test and the total number of ranks is 13.

From Appendix B, Table B.8 Wilcoxon T values:

Procedure:

1. In the Wilcoxon T values, locate n as 13.
2. Locate the value of 0.05 in α.
3. Locate the intersection value of the row and column. This gives the critical value.

The critical value for 0.05 the significance level is 21.

Decision rule:

If T≤21, reject the null hypothesis.
Otherwise, fail to reject the null hypothesis.

Answer 27

d.

Expert Solution

Answer 28

d.

Expert Solution

Answer 29

Expert Solution

Answer 30

e.

To determine

Make the necessary conclusions regarding the null hypothesis.

e.

Expert Solution

Answer to Problem 14E

The null hypothesis is not rejected.

Explanation of Solution

The sum of positive ranks is denoted as R⁺, and the sum of negative ranks is denoted as R^-.

Here,

R+=1+4+1+6+8+11=31

R−={13+9+11+7+4+1+10}=55

For the Wilcoxon signed-rank test, the test statistic will be obtained as follows:

T=Min(R+,R−)

In this context, the test statistic for sample size 13 is Min(31,55). Therefore, the test statistic is 31.

Conclusion:

Here, the test statistic is greater than the critical value.

Therefore, by the decision rule, fail to reject the null hypothesis.

Therefore, there is no enough evidence that the production using the new work environment has increased than the old.

Answer 31

e.

To determine

Make the necessary conclusions regarding the null hypothesis.

Answer 32

e.

Expert Solution

Answer to Problem 14E

The null hypothesis is not rejected.

Answer 33

e.

Expert Solution

Answer 34

e.

Expert Solution

Answer 35

Expert Solution

Answer 36

Explanation of Solution

The sum of positive ranks is denoted as R⁺, and the sum of negative ranks is denoted as R^-.

Here,

R+=1+4+1+6+8+11=31

R−={13+9+11+7+4+1+10}=55

For the Wilcoxon signed-rank test, the test statistic will be obtained as follows:

T=Min(R+,R−)

In this context, the test statistic for sample size 13 is Min(31,55). Therefore, the test statistic is 31.

Conclusion:

Here, the test statistic is greater than the critical value.

Therefore, by the decision rule, fail to reject the null hypothesis.

Therefore, there is no enough evidence that the production using the new work environment has increased than the old.

Answer 37

f.

To determine

State the assumption that has been assumed about the distribution of difference.

f.

Expert Solution

Explanation of Solution

In this context, none of the assumption is required for the distribution of difference.

Answer 38

f.

To determine

State the assumption that has been assumed about the distribution of difference.

Answer 39

f.

Expert Solution

Explanation of Solution

In this context, none of the assumption is required for the distribution of difference.

Answer 40

f.

Expert Solution

Answer 41

f.

Expert Solution

Answer 42

Expert Solution

Answer 43

Ch. 16 - Prob. 1SR Ch. 16 - Prob. 1E Ch. 16 - Prob. 2E Ch. 16 - Calorie Watchers has low-calorie breakfasts,...Ch. 16 - Prob. 4E Ch. 16 - Prob. 2SR Ch. 16 - Prob. 5E Ch. 16 - Prob. 6E Ch. 16 - Prob. 7E Ch. 16 - Prob. 8E

State the null hypothesis.

Solution Summary: The author states the null hypothesis and the alternative hypothesis.

Videos

State the null hypothesis.

Explanation of Solution

Decide the alternative hypothesis.

Explanation of Solution

Decide the level of significance.

Explanation of Solution

Provide the decision rule.

Explanation of Solution

Make the necessary conclusions regarding the null hypothesis.

Answer to Problem 14E

Explanation of Solution

State the assumption that has been assumed about the distribution of difference.

Explanation of Solution

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Chapter 16 Solutions