Which of the following is the correct first step when conducting a hypothesis test?

• A. Determine the sample $\mathrm{mean}$.
• B. State the $\mathrm{null}$ and $\mathrm{alternative}$ hypotheses.
• C. Draw a conclusion based on the $\mathrm{test}\mathrm{statistic}$.
• D. Calculate the $p-\mathrm{value}$.

Answer: (B)

Verified step by step guidance

1. Understand that the first step in any hypothesis test is to clearly state the null hypothesis (\(H_0\)) and the alternative hypothesis (\(H_a\)). These hypotheses represent the claims you want to test about the population parameter.
2. The null hypothesis (\(H_0\)) usually represents the status quo or no effect, while the alternative hypothesis (\(H_a\)) represents the claim you want to provide evidence for.
3. After stating the hypotheses, you would then collect data and calculate the sample statistic (such as the sample mean) to use in the test.
4. Next, you calculate the test statistic based on your sample data, which measures how far your sample statistic is from the null hypothesis value.
5. Finally, you calculate the p-value to determine the strength of evidence against the null hypothesis and then draw a conclusion based on this p-value.