Question

The P-value for a hypothesis test is shown. Use the P-value to decide whether to reject Hₒ when the level of significance is (a) α=0.01, (b) α=0.05, and (c) α=0.10. P=0.0538 (a) Do you reject or fail to reject Hₒ at the 0.01 level of significance? A. Fail to reject H_0 because the P-value, 0.0538, is less than α=0.01. B. Fail to reject H_0 because the P-value, 0.0538, is greater than α=0.01. C. Reject H0 because the P-value, 0.0538, is less than α=0.01. D. Reject H0 because the P-value, 0.0538, is greater than α=0.01.

Answer 1

To decide whether to reject or fail to reject the null hypothesis (H0) based on the p-value, you compare the p-value to the level of significance (α). Here are the decisions for each level of significance:

(a) α = 0.01:

You would reject H0 if the p-value is less than α, which means you would reject H0 if the p-value is less than 0.01.

Given that the p-value is 0.0538, which is greater than 0.01, you would fail to reject H0.

So, the correct answer for (a) is:

B. Fail to reject H0 because the P-value, 0.0538, is greater than α=0.01.

Explanation: