Suppose we run a statistical test. Which of the following is the correct first step in the process of hypothesis testing?

• A. Set the significance level after seeing the data.
• B. State the null $H$₀ and alternative $H$_a hypotheses.
• C. Draw a conclusion based on the test statistic.
• D. Calculate the $p$-value.

Answer: (B)

Verified step by step guidance

1. Understand that hypothesis testing begins with clearly defining the hypotheses you want to test. This involves stating the null hypothesis (\[H_0\]), which represents the default or no-effect assumption, and the alternative hypothesis (\[H_a\]), which represents the effect or difference you are testing for.
2. Recognize that setting the significance level (\[\alpha\]), which determines the threshold for rejecting the null hypothesis, should be done before collecting or examining the data to avoid bias.
3. After stating the hypotheses and setting the significance level, collect the data and calculate the test statistic, which summarizes the information in the data relevant to the hypotheses.
4. Use the test statistic to calculate the p-value, which measures the probability of observing data as extreme as, or more extreme than, what was observed, assuming the null hypothesis is true.
5. Finally, compare the p-value to the significance level to decide whether to reject or fail to reject the null hypothesis, and then draw a conclusion based on this comparison.