Concept explainers
(a)
The hypotheses for the significance test to check whether the average response time has decreased or not.
(a)
Answer to Problem 19E
For null hypothesis
Explanation of Solution
Given Information:
Population mean
Number of sample
By the null hypothesis,mean response time is equal to 6.7 minutes.
Thus,
By the alternative hypothesis mean response time is less than 6.7 minutes.
Thus,
Hence, for null hypothesis
(b)
Explain Type I error and Type II error and their consequences.
(b)
Answer to Problem 19E
In Type I error the response time has improved and the training does not have to be improved, but actually the training needs to improve.
In Type II error instead of the response time, training should be improve, but in reality the training should not be improved.
Explanation of Solution
In Type I error, when the null hypotheses is true than
Thus, the mean response time is equal to 6.7 minutes, but the test indicates that the mean response time is less.
Hence, the response time has improved and the training does not have to be improved, but actually the training needs to improve.
In Type II error,when the null hypotheses is true than rejection of
Thus, the mean response time is less than 6.7 minutes, while the test indicates that it is not less.
Hence, instead of the response time, training should be improve, but in reality the training should not be improved.
(c)
Explain which type of error is more serious.
(c)
Answer to Problem 19E
Type I error is more serious.
Explanation of Solution
The training has improved in Type II error but in Type I error, the training is not improved but in reality training needs to be improved in Type I error.
Hence,Type I error is more serious.
Chapter 9 Solutions
The Practice of Statistics for AP - 4th Edition
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