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

In a statistical hypothesis test, Null hypothesis is the neutral statement or the statment of null.

where as the alternative hypothesis is the complimentary to the null hypothesis. in the statistical test, the rejection region is framed based on the alternative hypothesis.

The alternative hypothesis in one direction or in both directions (non directional).

Taking the given example of insurance company older drivers are safer than younger ones.

Here we are testing the significance difference between sample mean values of older drives and young drives and take a decision based on the framed alternative hypothesis.

Here we want to test whethere older drivers are safter or not compared to younger ones.

The alternative hypothesis is : The Older drivers mean is greater than younger ones.

So here we test if difference of means exceeds certain extreme value in right side. if the difference is not extreme we accept otherwise reject.

If we set up alternative hypothesis as : There is no significance difference between younger and older drives.

The the difference of means value test whether it is extreme low or extrme high. in both cases we reject the null hypothesis.

The rejection region of the non-direction would be less compared to the dirctional

Here in this case, The directional will give more clear picture about the drivers. i.e whether old driver are greater than or not.

in the non dirctional case it conveys whether there is signficant difference or not only.

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