Which of the following is the initial step in conducting a hypothesis test?

• A. Draw a conclusion based on the results
• B. Calculate the test statistic
• C. Determine the $p$-value
• D. State the null and alternative hypotheses ($H_0$ and $H_a$)

Answer: (D)

Verified step by step guidance

1. Understand that the hypothesis testing process begins with formulating two competing statements: the null hypothesis (\[H_0\]) and the alternative hypothesis (\[H_a\]).
2. The null hypothesis (\[H_0\]) typically represents the status quo or a statement of no effect or no difference, while the alternative hypothesis (\[H_a\]) represents what you want to test or prove.
3. Clearly state these hypotheses before collecting any data or performing calculations, as they define the framework for the entire test.
4. After stating the hypotheses, the next steps involve collecting data, calculating the test statistic, determining the p-value, and finally drawing a conclusion based on the evidence.
5. Remember, without properly stating the null and alternative hypotheses first, the rest of the hypothesis testing process cannot be correctly carried out.