a.
Find the p-value and state the conclusion.
a.
Answer to Problem 36E
The p-value is 0.003.
The conclusion is “reject the null hypothesis”.
Explanation of Solution
Calculation:
The given information is that
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 −2.80.
Use Table 1: Cumulative probabilities for the standard normal distribution to find probability.
- Locate the value –2.8 in the first column.
- Locate the value 0.00 in the first row.
- The intersecting value that corresponds to–2.80 is 0.0026.
Thus, the p-value is 0.0026.
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.
Find the p-value and state the conclusion.
b.
Answer to Problem 36E
The p-value is 0.1151.
The conclusion is “do not reject the null hypothesis”.
Explanation of Solution
Calculation:
The given information is that
Test statistic:
Substitute
Thus, the value of the test statistic is −1.20.
Use Table 1: Cumulative probabilities for the standard normal distribution to find probability.
- Locate the value –1.2 in the first column.
- Locate the value 0.00 in the first row.
- The intersecting value that corresponds to the –1.20 is 0.1151.
Thus, the p-value is 0.1151.
Conclusion:
Here, the p-value is greater than the level of significance.
That is,
By the rejection rule, the null hypothesis is not rejected.
c.
Find the p-value and state the conclusion.
c.
Answer to Problem 36E
The p-value is 0.0228.
The conclusion is “reject the null hypothesis”.
Explanation of Solution
Calculation:
The given information is that
Test statistic:
Substitute
Thus, the value of the test statistic is −2.00.
Use Table 1: Cumulative probabilities for the standard normal distribution to find probability.
- Locate the value –2.0 in the first column.
- Locate the value 0.00 in the first row.
- The intersecting value that corresponds to the –2.00 is 0.0228.
Thus, the p-value is 0.0228.
From the output, the test statistic is −2.00 and the p-value is 0.0228.
Conclusion:
Here, the p-value is less than the level of significance.
That is,
By the rejection rule, the null hypothesis is rejected.
d.
Find the p-value and state the conclusion.
d.
Answer to Problem 36E
The p-value is 0.7881.
The conclusion is “do not reject the null hypothesis”.
Explanation of Solution
Calculation:
The given information is that
Test statistic:
Substitute
Thus, the value of the test statistic is 0.80.
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 0.00 in the first row.
- The intersecting value that corresponds to the 0.80 is 0.7881.
Thus, the p-value is 0.7881.
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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