Which statement describes the decision rule for a hypothesis test using p-values?

Which statement describes the decision rule for a hypothesis test using p-values?

• A. Reject H0 if p ≤ α; fail to reject otherwise.
• B. Fail to reject H0 if p ≤ α.
• C. Reject H0 if p > α.
• D. Reject H0 if p ≤ α; fail to reject otherwise.

Answer: (D)

When you test using a p-value, you compare the observed p-value to a preselected significance level α. If the p-value is less than or equal to α, you reject the null hypothesis; otherwise you fail to reject it. The p-value tells you how likely it is to see data as extreme as yours if the null is true—the smaller the p-value, the stronger the evidence against H0. Choosing α fixes how strong that evidence must be to declare a result statistically significant. For example, with α = 0.05, a p-value of 0.03 leads to rejection, while a p-value of 0.08 does not. We typically say “fail to reject” rather than “accept” H0, since lack of evidence isn’t proof that H0 is true.

When you test using a p-value, you compare the observed p-value to a preselected significance level α. If the p-value is less than or equal to α, you reject the null hypothesis; otherwise you fail to reject it. The p-value tells you how likely it is to see data as extreme as yours if the null is true—the smaller the p-value, the stronger the evidence against H0. Choosing α fixes how strong that evidence must be to declare a result statistically significant. For example, with α = 0.05, a p-value of 0.03 leads to rejection, while a p-value of 0.08 does not. We typically say “fail to reject” rather than “accept” H0, since lack of evidence isn’t proof that H0 is true.