SOLUTION: When computing a t-test, it is important to distinguish between directional and nondirectional hypotheses as the direction will determine the rejection regions. Describe how the re

Question 1186631: When computing a t-test, it is important to distinguish between directional and nondirectional hypotheses as the direction will determine the rejection regions. Describe how the rejection regions would differ according to the type of hypothesis you would use.
An insurance company asks you to determine whether older drivers are safer than younger ones. Provide a directional hypothesis related to this study. Then, explain how you would need to change the hypothesis so that it would be nondirectional. What happens to the rejection regions and why? Which of the two hypotheses do you think is more appropriate and why?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
There would be a unidirectional hypothesis with
Ho: Older same number of accidents or more than younger.
Ha: Older fewer accidents than younger.
The rejection region at the 5% level is all on the left side of the curve (fewer accidents than younger.) There is a larger area for rejection, so the absolute value of the test statistic can be smaller to reject the null hypothesis than the non-directional.
Non-directional:
Ho: older accidents=younger accidents
Ha:; the two are different or not equal
This one has a rejection region on both sides, so the absolute value of the test statistic is greater than in the first one to be in the rejection region
Given that older people and younger people both have more accidents, I would favor the nondirectional hypothesis which will look for a difference between the two. That is generally the preferred way to go, unless there is a strong suggestion one is better than the other and the study was set up that way.
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