If p > alpha, what is the appropriate action regarding the null hypothesis?

If p > alpha, what is the appropriate action regarding the null hypothesis?

• A. Reject the null hypothesis
• B. Retain (fail to reject) the null hypothesis
• C. Accept the null hypothesis
• D. It depends on sample size

Answer: (B)

The decision rule in hypothesis testing hinges on the p-value relative to the preselected significance level. The p-value tells you how compatible the observed data are with the null hypothesis under the assumption that it is true. If the p-value is greater than the significance level, the observed result is not sufficiently unlikely under the null to declare statistical significance. In that case you fail to reject the null hypothesis, meaning you retain it. It’s important to note that this does not prove the null is true; it simply means there isn’t enough evidence against it given the data and the chosen alpha. The idea that the decision depends on sample size isn’t correct in the sense of changing the rule itself—larger samples can affect the p-value and power, but the rule remains that a p-value exceeding alpha leads to failing to reject the null.

The decision rule in hypothesis testing hinges on the p-value relative to the preselected significance level. The p-value tells you how compatible the observed data are with the null hypothesis under the assumption that it is true. If the p-value is greater than the significance level, the observed result is not sufficiently unlikely under the null to declare statistical significance. In that case you fail to reject the null hypothesis, meaning you retain it.

It’s important to note that this does not prove the null is true; it simply means there isn’t enough evidence against it given the data and the chosen alpha. The idea that the decision depends on sample size isn’t correct in the sense of changing the rule itself—larger samples can affect the p-value and power, but the rule remains that a p-value exceeding alpha leads to failing to reject the null.