When computing a t-test, it is important to distinguish between directional and

Question

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?

Explanation / Answer

For a one tailed test the rejection region changes with the direction of the alternative hypothesis.

If the disrection is positive then the rejection region would be t (obtained)>t(observed)

If it is a left tailed (less than) alternative hypothesis then the rejection region would be t (obtained)<t(observed).

The null hypothesis is:

H0:The mean difference in the driving speed for older and younger drivers are same

Agaisnt the alternative hypothesis:

H1: The mean speed for youngers is greater than olders

Reject the null if t (obtained)>t(observed)

For a non directional hypothesis the alternative hypothesis:

H1: The mean speed for youngers is different from the olders

Reject the null if t (obtained)>+t(observed) or t (obtained)<-t(observed)

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