Which of the following correctly describes the steps for testing a hypothesis using the $p$-value approach, including verifying the requirements of the test?

• A. Calculate the $p$-value, state the null hypothesis, verify the requirements, and then always reject the null hypothesis if the $p$-value is less than $0.10$.
• B. Verify the requirements, state the alternative hypothesis only, calculate the test statistic, and accept the null hypothesis if the $p$-value is greater than the significance level.
• C. State the hypotheses, skip verifying requirements, calculate the $p$-value, and always accept the alternative hypothesis if the $p$-value is less than the significance level.
• D. State the null and alternative hypotheses, verify the requirements of the test, calculate the test statistic and $p$-value, compare the $p$-value to the significance level, and make a decision to reject or fail to reject the null hypothesis.

Answer: (D)

Verified step by step guidance

1. Step 1: State the null hypothesis (\(H_0\)) and the alternative hypothesis (\(H_a\)). The null hypothesis usually represents the status quo or no effect, while the alternative represents what you want to test for.
2. Step 2: Verify the requirements or assumptions of the test. This may include checking conditions such as sample size, normality, independence, or equal variances, depending on the test being used.
3. Step 3: Calculate the test statistic based on your sample data. The test statistic measures how far your sample data deviates from what is expected under the null hypothesis.
4. Step 4: Calculate the p-value, which is the probability of observing a test statistic as extreme as, or more extreme than, the one calculated, assuming the null hypothesis is true.
5. Step 5: Compare the p-value to the significance level (\(\alpha\)). If the p-value is less than or equal to \(\alpha\), reject the null hypothesis; otherwise, fail to reject the null hypothesis.