Question

For a hypothesis test of H0:p= 0.65 against the alternative Ha:p<0.65, the z test statistic is found to be -2.35. What can be said about his finding?

A.) The finding is significant at both a = 0.05 and a = 0.01.
B.) The finding is significant at a = 0.05, but not at a = 0.01
C.) The finding is significant at a = 0.01, but not at a = 0.05.
D.)The finding is not significant at a = 0.05 and a=0.01.
E.) The finding is inconclusive because we don't know the value of p.

Answer 1

The finding is significant at a = 0.05, but not at a = 0.01.

Step-by-step explanation:

The z-test statistic of -2.35 is used to test the null hypothesis that the population proportion (p) is equal to 0.65 against the alternative hypothesis that p is less than 0.65.

To determine the significance of the finding, we compare the z-test statistic to the critical value for a given significance level (alpha).

In this case, the critical value for a = 0.05 is -1.645, which means that if the z-test statistic is less than -1.645, we reject the null hypothesis.

Since -2.35 is less than -1.645, we reject the null hypothesis at the 0.05 significance level.

Therefore, the correct answer is B.) The finding is significant at a = 0.05, but not at a = 0.01.