Consider the following hypothesis test: H0: mean greater than or equal to 5 vs. H1: mean < 5. Suppose that you take a sample and conduct the test. You conclude that you can reject the null hypothesis.
What can you say about the results of the hypothesis test: H0: mean = 5 vs. H1: mean not equal to 5 tested using the same sample at the same level of significance?
a. reject H0 in the second test
b. do not reject H0 in the second test
c. need more information
d. reject H0 in the second test if p-value > .05, do not reject H0 if p-value < .05.
First, I will choose c. need more information.
Let me discuss each choice one by one.
First, from the given information in the first test, we have known that we would reject the null hypothesis and conclude that mean is less than 5.
So for choice a, we still can not say that we would reject H0 in the second test. The reason is that the alternative hypothesis is ...
The solution gives a detailed discussion on the logical relationship between rejecting and not rejecting a null hypothesis in the statistical test.