Question

How is the rejection region defined, and how is that related to the p value? When do you reject or fail to reject the null hypothesis? Why do you think statisticians are asked to complete hypothesis testing? Can you think of examples in courts, in medicine, or in your area?

Answer 1

Rejection region:

The rejection region is a range of values that when satisfied by the test statistic, the null hypothesis will be rejected.

Relation of P value:

That is also the range of values that when satisfied by the test statistic, gives out P values that are less than the significance level. Again, when the P value is less than the significance level.

Fail to reject the null hypothesis:

we reject the null hypothesis. If the test statistic is not in the rejection region, or consequently, the P value is greater than the significance level, we fail to reject the null hypothesis.

Hypothesis testing: I think statisticians are asked to do hypothesis testing becasue it is important to know if some events simply happened by chance or is there enough basis that it really happened for some reason.

Example: if we want to test if a new drug is effective, we would like to know whether or not the improvement in health of the patients is really due to the drug, and not simply due to other factors or chance, or maybe just a psychological effect.