Question

If, in a two-tail hypothesis test, the p-value is 0.0081, what is your statistical decision if you test the null hypothesis at the 0.01 level of significance?

a. Since the p-value is less than α, do not reject the null hypothesis.
b. Since the p-value is less than α, reject the null hypothesis.
c. Since the p-value is greater than α, reject the null hypothesis.
d. Since the p-value is greater than α, do not reject the null hypothesis.

Answer 1

In a two-tail hypothesis test with a p-value of 0.0081, which is less than the alpha level of 0.01, the correct decision is to reject the null hypothesis.

The correct option is b.

Step-by-step explanation:

If, in a two-tail hypothesis test, the p-value is 0.0081 and you are testing the null hypothesis at the 0.01 level of significance, you compare the p-value to the α (alpha) level. Since the p-value of 0.0081 is less than α of 0.01, the statistical decision is to reject the null hypothesis.

This is because a smaller p-value than the chosen significance level indicates that there is strong evidence against the null hypothesis, thus it should be rejected. This decision is based on the principle that if the p-value is less than or equal to the threshold alpha level, the result is statistically significant and the null hypothesis can be rejected.

The correct option is b.