In the steps of hypothesis testing, if the results indicate that the $p$-value is less than the significance level $\alpha$, what is the appropriate conclusion?

• A. Reject the null hypothesis
• B. Increase the sample size and repeat the test
• C. Accept the null hypothesis as true
• D. Fail to reject the null hypothesis

Answer: (A)

Verified step by step guidance

1. Understand the role of the p-value in hypothesis testing: the p-value measures the probability of obtaining test results at least as extreme as the observed results, assuming the null hypothesis is true.
2. Recall the significance level \( \alpha \), which is the threshold set before the test to decide whether to reject the null hypothesis. Common values are 0.05, 0.01, etc.
3. Compare the p-value to the significance level \( \alpha \): if \( \text{p-value} < \alpha \), it means the observed data is sufficiently unlikely under the null hypothesis.
4. Based on this comparison, the appropriate conclusion is to reject the null hypothesis because the evidence suggests it is not likely to be true.
5. Note that rejecting the null hypothesis does not prove it false with absolute certainty, but indicates strong evidence against it given the data and significance level.