a.
Find the p-value for
a.
Answer to Problem 14E
The p-value is 0.3844.
The conclusion is “do not reject the null hypothesis”.
Explanation of Solution
Calculation:
It is given that the sample size is
The hypotheses are given below:
Null hypothesis:
Alternative hypothesis:
Test statistic:
The formula for finding test statistic is as follows:
Here,
Substitute 23 for
Thus, the value of the test statistic is 0.87.
For p-value:
In this case, z is greater than 0. Therefore, the p-value is two times the upper tail area.
That is,
Use Table 1: Cumulative probabilities for the standard normal distribution to find probability.
- Locate the value 0.8 in the first column.
- Locate the value 0.07 in the first row.
- The intersecting value that corresponds to 0.87 is 0.8078.
Thus, the p-value is 0.3844.
Rejection rule:
If
If
Conclusion:
Here, the p-value is greater than the level of significance.
That is,
By the rejection rule, the null hypothesis is not rejected.
b.
Find the p-value for
b.
Answer to Problem 14E
The p-value is 0.0074.
The conclusion is “reject the null hypothesis”.
Explanation of Solution
Calculation:
Test statistic:
Substitute 25.1 for
Thus, the value of the test statistic is 2.68.
For p-value:
In this case, z is greater than 0. Therefore, the p-value is two times the upper tail area.
That is,
Use Table 1: Cumulative probabilities for the standard normal distribution to find probability.
- Locate the value 2.6 in the first column.
- Locate the value 0.08 in the first row.
- The intersecting value that corresponds to 2.68 is 0.9963.
Thus, the p-value is 0.0074.
Conclusion:
Here, the p-value is less than the level of significance.
That is,
By the rejection rule, the null hypothesis is rejected.
c.
Find the p-value for
c.
Answer to Problem 14E
The p-value is 0.083.
The conclusion is “do not reject the null hypothesis”.
Explanation of Solution
Calculation:
Test statistic:
Substitute 20 for
Thus, the value of the test statistic is –1.73.
For p-value:
In this case, z is less than 0. Therefore, the p-value is two times the lower tail area.
That is,
Use Table 1: Cumulative probabilities for the standard normal distribution to find probability.
- Locate the value –1.7 in the first column.
- Locate the value 0.03 in the first row.
- The intersecting value that corresponds to–1.73 is 0.0418.
Thus, the p-value is 0.0836.
Conclusion:
Here, the p-value is greater than the level of significance.
That is,
By the rejection rule, the null hypothesis is not rejected.
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Chapter 9 Solutions
Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)
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