
Concept explainers
To find: The test statistic and the corresponding P- value for the sample of size

Answer to Problem 93E
Solution: The test statistic is obtained as
Explanation of Solution
Calculation:
The assumption made that the
The proportions are provided as
To compute the statistic and the corresponding P-value, Minitab is used.
Follow the below mentioned steps in Minitab to perform the significance test,
Step 1: Go to ‘Stat’ then select ‘Basic Statistics’ and click on ‘2-Proportions’.
Step 2: In the dialogue box that appears select Summarized data and enter the provided sample size and number of successes in the respective fields.
Step 3: Click on ‘Options’ button and enter the confidence level as 95.
Step 4: Choose the Alternative as “Not equal” and click on OK twice.
The output shows that the test statistic is obtained as
To find: The test statistic and the corresponding P- value for the sample of size

Answer to Problem 93E
Solution: The test statistic is obtained as
Explanation of Solution
Calculation:
The assumption made that the sample size n is the common value of
The proportions are provided as
To compute the statistic and the corresponding P-value, Minitab is used.
Follow the below mentioned steps in Minitab to perform the significance test,
Step 1: Go to ‘Stat’ then select ‘Basic Statistics’ and click on ‘2-Proportions’.
Step 2: In the dialogue box that appears select Summarized data and enter the provided sample size and number of successes in the respective fields.
Step 3: Click on ‘Options’ button and enter the confidence level as 95.
Step 4: Choose the Alternative as “Not equal” and click on OK twice.
The output shows that the test statistic is obtained as
To find: The test statistic and the corresponding P- value for the sample of size

Answer to Problem 93E
Solution: The test statistic is obtained as
Explanation of Solution
Calculation:
The assumption made that the sample size n is the common value of
The proportions are provided as
To compute the statistic and the corresponding P-value, Minitab is used.
Follow the below mentioned steps in Minitab to perform the significance test,
Step 1: Go to ‘Stat’ then select ‘Basic Statistics’ and click on ‘2-Proportions’.
Step 2: In the dialogue box that appears select Summarized data and enter the provided sample size and number of successes in the respective fields.
Step 3: Click on ‘Options’ button and enter the confidence level as 95.
Step 4: Choose the Alternative as “Not equal” and click on OK twice.
The output shows that the test statistic is obtained as
To find: The test statistic and the corresponding P- value for the sample of size

Answer to Problem 93E
Solution: The test statistic is obtained as
Explanation of Solution
Calculation:
The assumption made that the sample size n is the common value of
The proportions are provided as
To compute the statistic and the corresponding P-value, Minitab is used.
Follow the below mentioned steps in Minitab to perform the significance test,
Step 1: Go to ‘Stat’ then select ‘Basic Statistics’ and click on ‘2-Proportions’.
Step 2: In the dialogue box that appears select Summarized data and enter the provided sample size and number of successes in the respective fields.
Step 3: Click on ‘Options’ button and enter the confidence level as 95.
Step 4: Choose the Alternative as “Not equal” and click on OK twice.
The output shows that the test statistic is obtained as
To find: The test statistic and the corresponding P- value for the sample of size

Answer to Problem 93E
Solution: The test statistic is obtained as
Explanation of Solution
Calculation:
The assumption made that the sample size n is the common value of
The proportions are provided as
To compute the statistic and the corresponding P-value, Minitab is used.
Follow the below mentioned steps in Minitab to perform the significance test,
Step 1: Go to ‘Stat’ then select ‘Basic Statistics’ and click on ‘2-Proportions’.
Step 2: In the dialogue box that appears select Summarized data and enter the provided sample size and number of successes in the respective fields.
Step 3: Click on ‘Options’ button and enter the confidence level as 95.
Step 4: Choose the Alternative as “Not equal” and click on OK twice.
The output shows that the test statistic is obtained as
To find: The test statistic and the corresponding P- value for the sample of size

Answer to Problem 93E
Solution: The test statistic is obtained as
Explanation of Solution
Calculation:
The assumption made that the sample size n is the common value of
The proportions are provided as
To compute the statistic and the corresponding P-value, Minitab is used.
Follow the below mentioned steps in Minitab to perform the significance test,
Step 1: Go to ‘Stat’ then select ‘Basic Statistics’ and click on ‘2-Proportions’.
Step 2: In the dialogue box that appears select Summarized data and enter the provided sample size and number of successes in the respective fields.
Step 3: Click on ‘Options’ button and enter the confidence level as 95.
Step 4: Choose the Alternative as “Not equal” and click on OK twice.
The output shows that the test statistic is obtained as
To find: The test statistic and the corresponding P- value for the sample of size

Answer to Problem 93E
Solution: The test statistic is obtained as
Explanation of Solution
Calculation:
The assumption made that the sample size n is the common value of
The proportions are provided as
To compute the statistic and the corresponding P-value, Minitab is used.
Follow the below mentioned steps in Minitab to perform the significance test,
Step 1: Go to ‘Stat’ then select ‘Basic Statistics’ and click on ‘2-Proportions’.
Step 2: In the dialogue box that appears select Summarized data and enter the provided sample size and number of successes in the respective fields.
Step 3: Click on ‘Options’ button and enter the confidence level as 95.
Step 4: Choose the Alternative as “Not equal” and click on OK twice.
The output shows that the test statistic is obtained as
To explain: The obtained results of test statistic and the corresponding P-value.

Answer to Problem 93E
Solution: The obtained results of test statistic and the corresponding P- value are summarized as:
n |
z |
P |
60 |
2.25 |
0.025 |
70 |
2.43 |
0.015 |
80 |
2.60 |
0.009 |
100 |
2.90 |
0.004 |
400 |
5.80 |
0.000 |
500 |
6.49 |
0.000 |
1000 |
9.18 |
0.000 |
Explanation of Solution
n |
z |
P |
60 |
2.25 |
0.025 |
70 |
2.43 |
0.015 |
80 |
2.60 |
0.009 |
100 |
2.90 |
0.004 |
400 |
5.80 |
0.000 |
500 |
6.49 |
0.000 |
1000 |
9.18 |
0.000 |
To explain: The effect of the sample size on the statistical significance for the same sample proportions.

Answer to Problem 93E
Solution: The difference of proportions becomes more significant as the sample size increases.
Explanation of Solution
The obtained values show that for small sample sizes, the results are not significant but for larger sample sizes, the result are significant and show that the sample proportions are significantly different.
Therefore, conclude that the difference becomes more significant as the sample size increases.
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Chapter 8 Solutions
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