If the p-value is 0.03 and alpha is 0.05, what decision should be made?

• A. Fail to reject the null.
• B. The result is inconclusive.
• C. Reject the null.
• D. Retain the alternative.

Answer: (C)

When deciding in hypothesis testing, you compare the p-value to the significance level. If the p-value is less than or equal to alpha, you reject the null hypothesis; otherwise you fail to reject it. Here, the p-value is 0.03 and alpha is 0.05. Since 0.03 ≤ 0.05, you reject the null hypothesis. This indicates statistically significant evidence at the 5% level in favor of the alternative.

Failing to reject would occur if the p-value were greater than 0.05. Saying the result is inconclusive isn’t the correct outcome at this p-value, and “retaining the alternative” isn’t a formal decision in hypothesis testing—you conclude there is evidence for the alternative when you reject the null.