Suppose you conduct a hypothesis test and your p-value is equal to $0.002$. What can you conclude if your significance level is $0.05$?

• A. Reject the null hypothesis because the p-value is less than the significance level ($p<\alpha$).
• B. The test is inconclusive because the p-value is too small.
• C. There is not enough evidence to support the alternative hypothesis.
• D. Fail to reject the null hypothesis because the p-value is greater than the significance level ($p>\alpha$).

Answer: (A)

Verified step by step guidance

1. Understand the meaning of the p-value: The p-value represents the probability of obtaining test results at least as extreme as the observed results, assuming the null hypothesis is true.
2. Identify the significance level (\(\alpha\)): This is the threshold for deciding whether to reject the null hypothesis. In this problem, \(\alpha\) = 0.05.
3. Compare the p-value to the significance level: If the p-value is less than \(\alpha\), it indicates that the observed data is unlikely under the null hypothesis.
4. Make a decision based on the comparison: Since the p-value (0.002) is less than the significance level (0.05), you reject the null hypothesis.
5. Interpret the conclusion: Rejecting the null hypothesis means there is sufficient evidence to support the alternative hypothesis at the 5% significance level.