The decision rule in a null hypothesis significance test hinges on comparing the p-value to the pre-determined significance level, denoted by $\alpha$. The null hypothesis (H₀) is rejected if the p-value is less than or equal to the significance level ($\alpha$).

Hypothesis Rejection Rule

The condition for rejecting the null hypothesis is:

$ p \le \alpha $

Significance Level ($\alpha$)

In this specific test, the significance level was set as:

$ \alpha = 0.01 $

Evaluating p-values for Rejection

We examine each provided p-value to see if it meets the rejection criterion ($p \le 0.01$):

• p = 0.004: Since $0.004 \le 0.01$, the null hypothesis is rejected. This corresponds to option A.
• p = 0.02: Since $0.02 > 0.01$, the null hypothesis is not rejected.
• p = 0.10: Since $0.10 > 0.01$, the null hypothesis is not rejected.
• p = 0.009: Since $0.009 \le 0.01$, the null hypothesis is rejected. This corresponds to option D.

Therefore, the null hypothesis would be rejected for p-values of $0.004$ and $0.009$.