Question

PLEASE HELP WILL GIVE EXTRA POINTS For a hypothesis test of H0: p = 0.40 against the alternative Ha: p > 0.40, the z test statistic is found to be 2.25. What can be said about this finding? The finding is significant at both α = 0.05 and α = 0.01. The finding is significant at α = 0.05 but not at α = 0.01. The finding is significant at α = 0.01 but not at α = 0.05. The finding is not significant at α = 0.05 and α = 0.01.

Answer 1

The finding is significant at α = 0.05 but not at α = 0.01.

Explanation:

We are given with the following hypothesis below;

Null Hypothesis,
`H_0` : p = 0.40 {means that the population proportion is equal to 40%}

Alternate Hypothesis,
`H_A` : p > 0.40 {means that the population proportion is greater than 40%}

The z-test statistics given to us is 2.25.

Now, at 0.05 level of significance, the z table gives a critical value of 1.645 for the right-tailed test.

Since the value of our test statistics is more than the critical value of z as 2.25 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Now, at 0.01 level of significance, the z table gives a critical value of 2.33 for the right-tailed test.

Since the value of our test statistics is less than the critical value of z as 2.25 < 2.33, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

This means that the finding is significant at α = 0.05 but not at α = 0.01.