Which of the following is typically the first step in hypothesis testing?

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

Answer: (A)

Verified step by step guidance

1. Understand that hypothesis testing is a structured process used to make decisions about population parameters based on sample data.
2. The very first step is to clearly 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 or prove.
3. After stating the hypotheses, the next steps involve selecting a significance level, collecting data, calculating the test statistic, and then determining the p-value.
4. Finally, you use the p-value or test statistic to decide whether to reject or fail to reject the null hypothesis, drawing a conclusion about the population.
5. Therefore, the initial and crucial step is to formulate the null and alternative hypotheses before proceeding with any calculations or data collection.