The test statistic and the p- value for sample size 10.

Question

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Answer 1

Question

Chapter 6, Problem 130E

Section 1

To determine

To find: The test statistic and the p- value for sample size 10.

Section 1

Expert Solution

Answer to Problem 130E

Solution: The value of Z test statistic is 1.58 and the p-value is 0.057.

Explanation of Solution

Calculation: To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 10 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 1.58 and the p-value is 0.057. Since the p-value is greater than significance level (0.05), the null hypothesis is accepted.

Section 2

To determine

To find: The test statistic and the p- value for sample size 20.

Section 2

Expert Solution

Answer to Problem 130E

Solution: The Z test statistic is 2.24 and the p-value 0.013.

Explanation of Solution

Calculation: To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 20 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 2.24 and the p-value is 0.013. Since the p-value is less than significance level (0.05), the null hypothesis is rejected.

Section 3

To determine

To find: The test statistic and the p- value for sample size 30.

Section 3

Expert Solution

Answer to Problem 130E

Solution: The Z test statistic is 2.74 and the p-value is 0.003.

Explanation of Solution

Calculation: To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 30 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 2.74 and the p-value is 0.003. Since the p-value is less than significance level (0.05), the null hypothesis is rejected.

Section 4

To determine

To find: The test statistic and the p- value for sample size 40.

Section 4

Expert Solution

Answer to Problem 130E

Solution: The Z test statistic is 3.16 and the p-value is 0.001.

Explanation of Solution

Calculation: To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 40 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 3.16 and the p-value is 0.001. Since the p-value is less than significance level (0.05), the null hypothesis is rejected.

Section 5

To determine

To find: The test statistic and the p- value for sample size 50.

Section 5

Expert Solution

Answer to Problem 130E

Solution: The Z test statistic is 3.54 and the p-value is0.000.

Explanation of Solution

To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 50 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 3.54 and the p-value is 0.000. Since the p-value is less than significance level (0.05), the null hypothesis is rejected.

Section 6

To determine

To graph: The values of test statistic versus sample size using the results of sections (1), (2), (3), (4) and (5).

Section 6

Expert Solution

Explanation of Solution

Graph: From the results of section 1 to 5, create a table for Sample size and test statistic.

Sample size	Test statistic
10	1.58
20	2.24
30	2.74
40	3.16
50	3.54

To plot the graph, follow the below mentioned steps in Minitab;

Step1: Enter the data of table in Minitab. Enter variable name as Sample size and test statistic.

Step 2: Go to Graph→Scatter plot

Step 3: In the dialog box select ‘simple’ then click Ok.

Step 4: In the new dialog box, enter ‘Test statistic’ as ‘Y variables’ ‘Sample size’ as ‘X variables’. Finally, click OK.

From the Minitab results, the graph is as follows,

Introduction to the Practice of Statistics, Chapter 6, Problem 130E , additional homework tip 1

Section 7:

To determine

To graph: The values of p-test versus sample size using the results of sections (1), (2), (3), (4), and (5).

Section 7:

Expert Solution

Explanation of Solution

Graph: From the results of section 1 to 5, create a table for Sample size and test statistic.

Sample size	p-value
10	0.057
20	0.013
30	0.003
40	0.001
50	0.000

To plot the graph, follow the below mentioned steps in Minitab;

Step1: Enter the data of table in Minitab. Enter variable name as Sample size and p-value.

Step 2: Go to Graph→Scatter plot

Step 3: In the dialog box select ‘simple’ then click Ok.

Step 4: In the new dialog box, enter ‘p-value’ under the field marked as ‘Y variables’ ‘Sample size’ under the field marked as ‘X variable’. Finally, click OK.

From the Minitab results, the graph is as follows,

Introduction to the Practice of Statistics, Chapter 6, Problem 130E , additional homework tip 2

To determine

To explain: The effect of the increment in sample size on test statistic and p- value.

Expert Solution

Answer to Problem 130E

Solution: As the sample size increases, the value of test statistic increases and the p- value decrease.

Explanation of Solution

From the scatter plots drawn above, it can be seen that the test statistic and the sample size are positively correlated whereas the p- value is negatively correlated.

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Answer 2

Question

Chapter 6, Problem 130E

Section 1

To determine

To find: The test statistic and the p- value for sample size 10.

Section 1

Expert Solution

Answer to Problem 130E

Solution: The value of Z test statistic is 1.58 and the p-value is 0.057.

Explanation of Solution

Calculation: To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 10 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 1.58 and the p-value is 0.057. Since the p-value is greater than significance level (0.05), the null hypothesis is accepted.

Section 2

To determine

To find: The test statistic and the p- value for sample size 20.

Section 2

Expert Solution

Answer to Problem 130E

Solution: The Z test statistic is 2.24 and the p-value 0.013.

Explanation of Solution

Calculation: To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 20 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 2.24 and the p-value is 0.013. Since the p-value is less than significance level (0.05), the null hypothesis is rejected.

Section 3

To determine

To find: The test statistic and the p- value for sample size 30.

Section 3

Expert Solution

Answer to Problem 130E

Solution: The Z test statistic is 2.74 and the p-value is 0.003.

Explanation of Solution

Calculation: To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 30 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 2.74 and the p-value is 0.003. Since the p-value is less than significance level (0.05), the null hypothesis is rejected.

Section 4

To determine

To find: The test statistic and the p- value for sample size 40.

Section 4

Expert Solution

Answer to Problem 130E

Solution: The Z test statistic is 3.16 and the p-value is 0.001.

Explanation of Solution

Calculation: To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 40 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 3.16 and the p-value is 0.001. Since the p-value is less than significance level (0.05), the null hypothesis is rejected.

Section 5

To determine

To find: The test statistic and the p- value for sample size 50.

Section 5

Expert Solution

Answer to Problem 130E

Solution: The Z test statistic is 3.54 and the p-value is0.000.

Explanation of Solution

To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 50 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 3.54 and the p-value is 0.000. Since the p-value is less than significance level (0.05), the null hypothesis is rejected.

Section 6

To determine

To graph: The values of test statistic versus sample size using the results of sections (1), (2), (3), (4) and (5).

Section 6

Expert Solution

Explanation of Solution

Graph: From the results of section 1 to 5, create a table for Sample size and test statistic.

Sample size	Test statistic
10	1.58
20	2.24
30	2.74
40	3.16
50	3.54

To plot the graph, follow the below mentioned steps in Minitab;

Step1: Enter the data of table in Minitab. Enter variable name as Sample size and test statistic.

Step 2: Go to Graph→Scatter plot

Step 3: In the dialog box select ‘simple’ then click Ok.

Step 4: In the new dialog box, enter ‘Test statistic’ as ‘Y variables’ ‘Sample size’ as ‘X variables’. Finally, click OK.

From the Minitab results, the graph is as follows,

Introduction to the Practice of Statistics, Chapter 6, Problem 130E , additional homework tip 1

Section 7:

To determine

To graph: The values of p-test versus sample size using the results of sections (1), (2), (3), (4), and (5).

Section 7:

Expert Solution

Explanation of Solution

Graph: From the results of section 1 to 5, create a table for Sample size and test statistic.

Sample size	p-value
10	0.057
20	0.013
30	0.003
40	0.001
50	0.000

To plot the graph, follow the below mentioned steps in Minitab;

Step1: Enter the data of table in Minitab. Enter variable name as Sample size and p-value.

Step 2: Go to Graph→Scatter plot

Step 3: In the dialog box select ‘simple’ then click Ok.

Step 4: In the new dialog box, enter ‘p-value’ under the field marked as ‘Y variables’ ‘Sample size’ under the field marked as ‘X variable’. Finally, click OK.

From the Minitab results, the graph is as follows,

Introduction to the Practice of Statistics, Chapter 6, Problem 130E , additional homework tip 2

To determine

To explain: The effect of the increment in sample size on test statistic and p- value.

Expert Solution

Answer to Problem 130E

Solution: As the sample size increases, the value of test statistic increases and the p- value decrease.

Explanation of Solution

From the scatter plots drawn above, it can be seen that the test statistic and the sample size are positively correlated whereas the p- value is negatively correlated.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Chapter 6, Problem 130E

Section 1

To determine

To find: The test statistic and the p- value for sample size 10.

Section 1

Expert Solution

Answer to Problem 130E

Solution: The value of Z test statistic is 1.58 and the p-value is 0.057.

Explanation of Solution

Calculation: To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 10 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 1.58 and the p-value is 0.057. Since the p-value is greater than significance level (0.05), the null hypothesis is accepted.

Section 2

To determine

To find: The test statistic and the p- value for sample size 20.

Section 2

Expert Solution

Answer to Problem 130E

Solution: The Z test statistic is 2.24 and the p-value 0.013.

Explanation of Solution

Calculation: To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 20 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 2.24 and the p-value is 0.013. Since the p-value is less than significance level (0.05), the null hypothesis is rejected.

Section 3

To determine

To find: The test statistic and the p- value for sample size 30.

Section 3

Expert Solution

Answer to Problem 130E

Solution: The Z test statistic is 2.74 and the p-value is 0.003.

Explanation of Solution

Calculation: To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 30 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 2.74 and the p-value is 0.003. Since the p-value is less than significance level (0.05), the null hypothesis is rejected.

Section 4

To determine

To find: The test statistic and the p- value for sample size 40.

Section 4

Expert Solution

Answer to Problem 130E

Solution: The Z test statistic is 3.16 and the p-value is 0.001.

Explanation of Solution

Calculation: To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 40 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 3.16 and the p-value is 0.001. Since the p-value is less than significance level (0.05), the null hypothesis is rejected.

Section 5

To determine

To find: The test statistic and the p- value for sample size 50.

Section 5

Expert Solution

Answer to Problem 130E

Solution: The Z test statistic is 3.54 and the p-value is0.000.

Explanation of Solution

To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 50 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 3.54 and the p-value is 0.000. Since the p-value is less than significance level (0.05), the null hypothesis is rejected.

Section 6

To determine

To graph: The values of test statistic versus sample size using the results of sections (1), (2), (3), (4) and (5).

Section 6

Expert Solution

Explanation of Solution

Graph: From the results of section 1 to 5, create a table for Sample size and test statistic.

Sample size	Test statistic
10	1.58
20	2.24
30	2.74
40	3.16
50	3.54

To plot the graph, follow the below mentioned steps in Minitab;

Step1: Enter the data of table in Minitab. Enter variable name as Sample size and test statistic.

Step 2: Go to Graph→Scatter plot

Step 3: In the dialog box select ‘simple’ then click Ok.

Step 4: In the new dialog box, enter ‘Test statistic’ as ‘Y variables’ ‘Sample size’ as ‘X variables’. Finally, click OK.

From the Minitab results, the graph is as follows,

Introduction to the Practice of Statistics, Chapter 6, Problem 130E , additional homework tip 1

Section 7:

To determine

To graph: The values of p-test versus sample size using the results of sections (1), (2), (3), (4), and (5).

Section 7:

Expert Solution

Explanation of Solution

Graph: From the results of section 1 to 5, create a table for Sample size and test statistic.

Sample size	p-value
10	0.057
20	0.013
30	0.003
40	0.001
50	0.000

To plot the graph, follow the below mentioned steps in Minitab;

Step1: Enter the data of table in Minitab. Enter variable name as Sample size and p-value.

Step 2: Go to Graph→Scatter plot

Step 3: In the dialog box select ‘simple’ then click Ok.

Step 4: In the new dialog box, enter ‘p-value’ under the field marked as ‘Y variables’ ‘Sample size’ under the field marked as ‘X variable’. Finally, click OK.

From the Minitab results, the graph is as follows,

Introduction to the Practice of Statistics, Chapter 6, Problem 130E , additional homework tip 2

To determine

To explain: The effect of the increment in sample size on test statistic and p- value.

Expert Solution

Answer to Problem 130E

Solution: As the sample size increases, the value of test statistic increases and the p- value decrease.

Explanation of Solution

From the scatter plots drawn above, it can be seen that the test statistic and the sample size are positively correlated whereas the p- value is negatively correlated.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 6, Problem 130E

Section 1

To determine

To find: The test statistic and the p- value for sample size 10.

Section 1

Expert Solution

Answer to Problem 130E

Solution: The value of Z test statistic is 1.58 and the p-value is 0.057.

Explanation of Solution

Calculation: To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 10 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 1.58 and the p-value is 0.057. Since the p-value is greater than significance level (0.05), the null hypothesis is accepted.

Section 2

To determine

To find: The test statistic and the p- value for sample size 20.

Section 2

Expert Solution

Answer to Problem 130E

Solution: The Z test statistic is 2.24 and the p-value 0.013.

Explanation of Solution

Calculation: To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 20 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 2.24 and the p-value is 0.013. Since the p-value is less than significance level (0.05), the null hypothesis is rejected.

Section 3

To determine

To find: The test statistic and the p- value for sample size 30.

Section 3

Expert Solution

Answer to Problem 130E

Solution: The Z test statistic is 2.74 and the p-value is 0.003.

Explanation of Solution

Calculation: To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 30 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 2.74 and the p-value is 0.003. Since the p-value is less than significance level (0.05), the null hypothesis is rejected.

Section 4

To determine

To find: The test statistic and the p- value for sample size 40.

Section 4

Expert Solution

Answer to Problem 130E

Solution: The Z test statistic is 3.16 and the p-value is 0.001.

Explanation of Solution

Calculation: To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 40 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 3.16 and the p-value is 0.001. Since the p-value is less than significance level (0.05), the null hypothesis is rejected.

Section 5

To determine

To find: The test statistic and the p- value for sample size 50.

Section 5

Expert Solution

Answer to Problem 130E

Solution: The Z test statistic is 3.54 and the p-value is0.000.

Explanation of Solution

To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 50 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 3.54 and the p-value is 0.000. Since the p-value is less than significance level (0.05), the null hypothesis is rejected.

Section 6

To determine

To graph: The values of test statistic versus sample size using the results of sections (1), (2), (3), (4) and (5).

Section 6

Expert Solution

Explanation of Solution

Graph: From the results of section 1 to 5, create a table for Sample size and test statistic.

Sample size	Test statistic
10	1.58
20	2.24
30	2.74
40	3.16
50	3.54

To plot the graph, follow the below mentioned steps in Minitab;

Step1: Enter the data of table in Minitab. Enter variable name as Sample size and test statistic.

Step 2: Go to Graph→Scatter plot

Step 3: In the dialog box select ‘simple’ then click Ok.

Step 4: In the new dialog box, enter ‘Test statistic’ as ‘Y variables’ ‘Sample size’ as ‘X variables’. Finally, click OK.

From the Minitab results, the graph is as follows,

Introduction to the Practice of Statistics, Chapter 6, Problem 130E , additional homework tip 1

Section 7:

To determine

To graph: The values of p-test versus sample size using the results of sections (1), (2), (3), (4), and (5).

Section 7:

Expert Solution

Explanation of Solution

Graph: From the results of section 1 to 5, create a table for Sample size and test statistic.

Sample size	p-value
10	0.057
20	0.013
30	0.003
40	0.001
50	0.000

To plot the graph, follow the below mentioned steps in Minitab;

Step1: Enter the data of table in Minitab. Enter variable name as Sample size and p-value.

Step 2: Go to Graph→Scatter plot

Step 3: In the dialog box select ‘simple’ then click Ok.

Step 4: In the new dialog box, enter ‘p-value’ under the field marked as ‘Y variables’ ‘Sample size’ under the field marked as ‘X variable’. Finally, click OK.

From the Minitab results, the graph is as follows,

Introduction to the Practice of Statistics, Chapter 6, Problem 130E , additional homework tip 2

To determine

To explain: The effect of the increment in sample size on test statistic and p- value.

Expert Solution

Answer to Problem 130E

Solution: As the sample size increases, the value of test statistic increases and the p- value decrease.

Explanation of Solution

From the scatter plots drawn above, it can be seen that the test statistic and the sample size are positively correlated whereas the p- value is negatively correlated.

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Answer 5

Chapter 6, Problem 130E

Section 1

To determine

To find: The test statistic and the p- value for sample size 10.

Section 1

Expert Solution

Answer to Problem 130E

Solution: The value of Z test statistic is 1.58 and the p-value is 0.057.

Explanation of Solution

Calculation: To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 10 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 1.58 and the p-value is 0.057. Since the p-value is greater than significance level (0.05), the null hypothesis is accepted.

Section 2

To determine

To find: The test statistic and the p- value for sample size 20.

Section 2

Expert Solution

Answer to Problem 130E

Solution: The Z test statistic is 2.24 and the p-value 0.013.

Explanation of Solution

Calculation: To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 20 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 2.24 and the p-value is 0.013. Since the p-value is less than significance level (0.05), the null hypothesis is rejected.

Section 3

To determine

To find: The test statistic and the p- value for sample size 30.

Section 3

Expert Solution

Answer to Problem 130E

Solution: The Z test statistic is 2.74 and the p-value is 0.003.

Explanation of Solution

Calculation: To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 30 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 2.74 and the p-value is 0.003. Since the p-value is less than significance level (0.05), the null hypothesis is rejected.

Section 4

To determine

To find: The test statistic and the p- value for sample size 40.

Section 4

Expert Solution

Answer to Problem 130E

Solution: The Z test statistic is 3.16 and the p-value is 0.001.

Explanation of Solution

Calculation: To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 40 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 3.16 and the p-value is 0.001. Since the p-value is less than significance level (0.05), the null hypothesis is rejected.

Section 5

To determine

To find: The test statistic and the p- value for sample size 50.

Section 5

Expert Solution

Answer to Problem 130E

Solution: The Z test statistic is 3.54 and the p-value is0.000.

Explanation of Solution

To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 50 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 3.54 and the p-value is 0.000. Since the p-value is less than significance level (0.05), the null hypothesis is rejected.

Section 6

To determine

To graph: The values of test statistic versus sample size using the results of sections (1), (2), (3), (4) and (5).

Section 6

Expert Solution

Explanation of Solution

Graph: From the results of section 1 to 5, create a table for Sample size and test statistic.

Sample size	Test statistic
10	1.58
20	2.24
30	2.74
40	3.16
50	3.54

To plot the graph, follow the below mentioned steps in Minitab;

Step1: Enter the data of table in Minitab. Enter variable name as Sample size and test statistic.

Step 2: Go to Graph→Scatter plot

Step 3: In the dialog box select ‘simple’ then click Ok.

Step 4: In the new dialog box, enter ‘Test statistic’ as ‘Y variables’ ‘Sample size’ as ‘X variables’. Finally, click OK.

From the Minitab results, the graph is as follows,

Introduction to the Practice of Statistics, Chapter 6, Problem 130E , additional homework tip 1

Section 7:

To determine

To graph: The values of p-test versus sample size using the results of sections (1), (2), (3), (4), and (5).

Section 7:

Expert Solution

Explanation of Solution

Graph: From the results of section 1 to 5, create a table for Sample size and test statistic.

Sample size	p-value
10	0.057
20	0.013
30	0.003
40	0.001
50	0.000

To plot the graph, follow the below mentioned steps in Minitab;

Step1: Enter the data of table in Minitab. Enter variable name as Sample size and p-value.

Step 2: Go to Graph→Scatter plot

Step 3: In the dialog box select ‘simple’ then click Ok.

Step 4: In the new dialog box, enter ‘p-value’ under the field marked as ‘Y variables’ ‘Sample size’ under the field marked as ‘X variable’. Finally, click OK.

From the Minitab results, the graph is as follows,

Introduction to the Practice of Statistics, Chapter 6, Problem 130E , additional homework tip 2

To determine

To explain: The effect of the increment in sample size on test statistic and p- value.

Expert Solution

Answer to Problem 130E

Solution: As the sample size increases, the value of test statistic increases and the p- value decrease.

Explanation of Solution

From the scatter plots drawn above, it can be seen that the test statistic and the sample size are positively correlated whereas the p- value is negatively correlated.

Answer 6

Chapter 6, Problem 130E

Section 1

To determine

To find: The test statistic and the p- value for sample size 10.

Section 1

Expert Solution

Answer to Problem 130E

Solution: The value of Z test statistic is 1.58 and the p-value is 0.057.

Explanation of Solution

Calculation: To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 10 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 1.58 and the p-value is 0.057. Since the p-value is greater than significance level (0.05), the null hypothesis is accepted.

Answer 7

Chapter 6, Problem 130E

Section 1

To determine

To find: The test statistic and the p- value for sample size 10.

Answer 8

Section 1

Expert Solution

Answer to Problem 130E

Solution: The value of Z test statistic is 1.58 and the p-value is 0.057.

Answer 9

Section 1

Expert Solution

Answer 10

Section 1

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Calculation: To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 10 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 1.58 and the p-value is 0.057. Since the p-value is greater than significance level (0.05), the null hypothesis is accepted.

Answer 13

Section 2

To determine

To find: The test statistic and the p- value for sample size 20.

Section 2

Expert Solution

Answer to Problem 130E

Solution: The Z test statistic is 2.24 and the p-value 0.013.

Explanation of Solution

Calculation: To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 20 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 2.24 and the p-value is 0.013. Since the p-value is less than significance level (0.05), the null hypothesis is rejected.

Answer 14

Section 2

To determine

To find: The test statistic and the p- value for sample size 20.

Answer 15

Section 2

Expert Solution

Answer to Problem 130E

Solution: The Z test statistic is 2.24 and the p-value 0.013.

Answer 16

Section 2

Expert Solution

Answer 17

Section 2

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Calculation: To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 20 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 2.24 and the p-value is 0.013. Since the p-value is less than significance level (0.05), the null hypothesis is rejected.

Answer 20

Section 3

To determine

To find: The test statistic and the p- value for sample size 30.

Section 3

Expert Solution

Answer to Problem 130E

Solution: The Z test statistic is 2.74 and the p-value is 0.003.

Explanation of Solution

Calculation: To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 30 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 2.74 and the p-value is 0.003. Since the p-value is less than significance level (0.05), the null hypothesis is rejected.

Answer 21

Section 3

To determine

To find: The test statistic and the p- value for sample size 30.

Answer 22

Section 3

Expert Solution

Answer to Problem 130E

Solution: The Z test statistic is 2.74 and the p-value is 0.003.

Answer 23

Section 3

Expert Solution

Answer 24

Section 3

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Calculation: To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 30 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 2.74 and the p-value is 0.003. Since the p-value is less than significance level (0.05), the null hypothesis is rejected.

Answer 27

Section 4

To determine

To find: The test statistic and the p- value for sample size 40.

Section 4

Expert Solution

Answer to Problem 130E

Solution: The Z test statistic is 3.16 and the p-value is 0.001.

Explanation of Solution

Calculation: To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 40 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 3.16 and the p-value is 0.001. Since the p-value is less than significance level (0.05), the null hypothesis is rejected.

Answer 28

Section 4

To determine

To find: The test statistic and the p- value for sample size 40.

Answer 29

Section 4

Expert Solution

Answer to Problem 130E

Solution: The Z test statistic is 3.16 and the p-value is 0.001.

Answer 30

Section 4

Expert Solution

Answer 31

Section 4

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

Calculation: To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 40 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 3.16 and the p-value is 0.001. Since the p-value is less than significance level (0.05), the null hypothesis is rejected.

Answer 34

Section 5

To determine

To find: The test statistic and the p- value for sample size 50.

Section 5

Expert Solution

Answer to Problem 130E

Solution: The Z test statistic is 3.54 and the p-value is0.000.

Explanation of Solution

To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 50 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 3.54 and the p-value is 0.000. Since the p-value is less than significance level (0.05), the null hypothesis is rejected.

Answer 35

Section 5

To determine

To find: The test statistic and the p- value for sample size 50.

Answer 36

Section 5

Expert Solution

Answer to Problem 130E

Solution: The Z test statistic is 3.54 and the p-value is0.000.

Answer 37

Section 5

Expert Solution

Answer 38

Section 5

Expert Solution

Answer 39

Expert Solution

Answer 40

Explanation of Solution

To calculate the test statistic and the p-value follow the below mentioned steps in Minitab;

Step 1: Go to Stat→Basic statistics→1-sample Z.

Step 2: In the dialog box that appears select ‘Summarized data’. Then enter 50 under the field marked as ‘Sample size’, 16 under the field marked as ‘Standard deviation’ and 8 under ‘Mean’ field.

Step 3: Click on ‘Perform Hypothesised test’. Enter 0 under the field marked as ‘Hypothesised mean’. Click on ‘option’.

Step 4: In the dialog box that appears, enter ‘95.0’ under the field marked as ‘Confidence level’ and select ‘greater than’ under the field marked as ‘Alternative hypothesis’. Finally, click on ‘OK’.

From Minitab results, The Z test statistic is 3.54 and the p-value is 0.000. Since the p-value is less than significance level (0.05), the null hypothesis is rejected.

Answer 41

Section 6

To determine

To graph: The values of test statistic versus sample size using the results of sections (1), (2), (3), (4) and (5).

Section 6

Expert Solution

Explanation of Solution

Graph: From the results of section 1 to 5, create a table for Sample size and test statistic.

Sample size	Test statistic
10	1.58
20	2.24
30	2.74
40	3.16
50	3.54

To plot the graph, follow the below mentioned steps in Minitab;

Step1: Enter the data of table in Minitab. Enter variable name as Sample size and test statistic.

Step 2: Go to Graph→Scatter plot

Step 3: In the dialog box select ‘simple’ then click Ok.

Step 4: In the new dialog box, enter ‘Test statistic’ as ‘Y variables’ ‘Sample size’ as ‘X variables’. Finally, click OK.

From the Minitab results, the graph is as follows,

Introduction to the Practice of Statistics, Chapter 6, Problem 130E , additional homework tip 1

Answer 42

Section 6

To determine

To graph: The values of test statistic versus sample size using the results of sections (1), (2), (3), (4) and (5).

Answer 43

Section 6

Expert Solution

Explanation of Solution

Graph: From the results of section 1 to 5, create a table for Sample size and test statistic.

Sample size	Test statistic
10	1.58
20	2.24
30	2.74
40	3.16
50	3.54

To plot the graph, follow the below mentioned steps in Minitab;

Step1: Enter the data of table in Minitab. Enter variable name as Sample size and test statistic.

Step 2: Go to Graph→Scatter plot

Step 3: In the dialog box select ‘simple’ then click Ok.

Step 4: In the new dialog box, enter ‘Test statistic’ as ‘Y variables’ ‘Sample size’ as ‘X variables’. Finally, click OK.

From the Minitab results, the graph is as follows,

Introduction to the Practice of Statistics, Chapter 6, Problem 130E , additional homework tip 1

Answer 44

Section 6

Expert Solution

Answer 45

Section 6

Expert Solution

Answer 46

Expert Solution

Answer 47

Section 7:

To determine

To graph: The values of p-test versus sample size using the results of sections (1), (2), (3), (4), and (5).

Section 7:

Expert Solution

Explanation of Solution

Graph: From the results of section 1 to 5, create a table for Sample size and test statistic.

Sample size	p-value
10	0.057
20	0.013
30	0.003
40	0.001
50	0.000

To plot the graph, follow the below mentioned steps in Minitab;

Step1: Enter the data of table in Minitab. Enter variable name as Sample size and p-value.

Step 2: Go to Graph→Scatter plot

Step 3: In the dialog box select ‘simple’ then click Ok.

Step 4: In the new dialog box, enter ‘p-value’ under the field marked as ‘Y variables’ ‘Sample size’ under the field marked as ‘X variable’. Finally, click OK.

From the Minitab results, the graph is as follows,

Introduction to the Practice of Statistics, Chapter 6, Problem 130E , additional homework tip 2

Answer 48

Section 7:

To determine

To graph: The values of p-test versus sample size using the results of sections (1), (2), (3), (4), and (5).

Answer 49

Section 7:

Expert Solution

Explanation of Solution

Graph: From the results of section 1 to 5, create a table for Sample size and test statistic.

Sample size	p-value
10	0.057
20	0.013
30	0.003
40	0.001
50	0.000

To plot the graph, follow the below mentioned steps in Minitab;

Step1: Enter the data of table in Minitab. Enter variable name as Sample size and p-value.

Step 2: Go to Graph→Scatter plot

Step 3: In the dialog box select ‘simple’ then click Ok.

Step 4: In the new dialog box, enter ‘p-value’ under the field marked as ‘Y variables’ ‘Sample size’ under the field marked as ‘X variable’. Finally, click OK.

From the Minitab results, the graph is as follows,

Introduction to the Practice of Statistics, Chapter 6, Problem 130E , additional homework tip 2

Answer 50

Section 7:

Expert Solution

Answer 51

Section 7:

Expert Solution

Answer 52

Expert Solution

Answer 53

To determine

To explain: The effect of the increment in sample size on test statistic and p- value.

Expert Solution

Answer to Problem 130E

Solution: As the sample size increases, the value of test statistic increases and the p- value decrease.

Explanation of Solution

From the scatter plots drawn above, it can be seen that the test statistic and the sample size are positively correlated whereas the p- value is negatively correlated.

Answer 54

To determine

To explain: The effect of the increment in sample size on test statistic and p- value.

Answer 55

Expert Solution

Answer to Problem 130E

Solution: As the sample size increases, the value of test statistic increases and the p- value decrease.

Answer 56

Expert Solution

Answer 57

Expert Solution

Answer 58

Expert Solution

Answer 59

Explanation of Solution

From the scatter plots drawn above, it can be seen that the test statistic and the sample size are positively correlated whereas the p- value is negatively correlated.