a.
Find the p-value and state the conclusion.
a.
![Check Mark](/static/check-mark.png)
Answer to Problem 26E
The p-value is 0.039.
The conclusion is “reject the null hypothesis”.
Explanation of Solution
Calculation:
The given information is the
The hypotheses are given below:
Null hypothesis:
Alternative hypothesis:
Test statistic:
The formula for finding test statistic is as follows:
Here,
Substitute
Thus, the value of the test statistic is 2.10.
The degrees of freedom is,
Software Procedure:
Step-by-step procedure to obtain the probability value using Excel:
- Open an EXCEL sheet and select the cell A1.
- Enter the formula =T.DIST.2T(2.10,64) in the cell A1.
- Press Enter.
Output using the EXCEL software is given below:
From the output, the exact p-value is approximately 0.040.
Rejection rule:
If
If
Conclusion:
Here, the p-value is less than the level of significance.
That is,
By the rejection rule, the null hypothesis is rejected.
b.
Calculate the p-value and draw the conclusion.
b.
![Check Mark](/static/check-mark.png)
Answer to Problem 26E
The p-value is 0.013.
The conclusion is “reject the null hypothesis”.
Explanation of Solution
Calculation:
The given information is that the sample size is
Test statistic:
Substitute
Thus, the value of the test statistic is –2.57.
From part (a), the degrees of freedom is 64.
Software Procedure:
Step-by-step procedure to obtain the probability value using Excel:
- Open an EXCEL sheet and select the cell A1.
- Enter the formula =T.DIST.2T(2.57,64) in the cell A1.
- Press Enter.
Output using the EXCEL software is given below:
From the output, the exact p-value is approximately 0.0125.
Conclusion:
Here, the p-value is less than the level of significance.
That is,
By the rejection rule, the null hypothesis is rejected.
c.
Obtain the p-value and claim the conclusion.
c.
![Check Mark](/static/check-mark.png)
Answer to Problem 26E
The p-value is 0.130.
The conclusion is “do not reject the null hypothesis”.
Explanation of Solution
Calculation:
The given information is that the sample size is
Test statistic:
Substitute
Thus, the value of the test statistic is 1.54.
From part (a), the degrees of freedom is 64.
Software Procedure:
Step-by-step procedure to obtain the probability value using Excel:
- Open an EXCEL sheet and select the cell A1.
- Enter the formula =T.DIST.2T(1.54,64) in the cell A1.
- Press Enter.
Output using the EXCEL software is given below:
From the output, the exact p-value is approximately 0.01285.
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
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