If the cutoffs for a z test score are -2.58 and 2.58, determine whether you would reject or fail to reject the null hypothesis for z score .95

The cutoffs are given as -2.58 or 2.58. This creates a critical region that is in two parts: any test score below -2.58 or above 2.58 is in the critical region.

If a test score is in the critical region you would reject the null hypothesis. Essentially you are saying that if the null hypothesis were correct, a result as the one you are testing should not happen, at least within you level of certainty.

Here your score is in the non-critical region. This implies that the result could easily occur by chance if the null hypothesis was correct.

Thus if the test score is z=.95 you would not reject the null hypothesis. ( Given the critical points +-2.58)

** You cannot say that the alternative hypothesis is false. At most you can say that there is insufficient evidence to support the alternative hypothesis.**