How is the rejection region defined and how is that related to the z-score and 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

Using P ≤ .05, if the probability the results would occur by chance is P > .05, you would accept the null hypothesis.

By using any level of significance, if it equals or is less than that level, you would be assuming that the results indicate significant differences. Significant differences are unlikely to be due to chance alone. Although there is a small probability (alpha error) that the null hypothesis (no differences) is really true, you are assuming that it is not true in this instance.

By replicating experiments, if the same results are repeated, we can be even more sure of their significance. For example, if the same level of significance was found at P = .01 for 4 studies, the probability that all 4 would have found the same results solely by chance = (.01)^4 = .01 * .01 * .01 * .01 = .000000001 = 1 time in a billion that these results all would occur by chance. At that point, I can be very certain in the significance of rejecting the null hypothesis.

Once you know the Z score, the P values are found in a table in the back of your statistics text labeled something like "areas under normal distribution."

I can't know what "you think." I'll leave the examples up to you.