Which of the following does not need to be known in order to compute the $p$-value in a hypothesis test?

• A. Whether the test is one-tailed or two-tailed
• B. The sampling distribution of the test statistic under the null hypothesis
• C. The significance level $\alpha$
• D. The observed value of the test statistic

Answer: (C)

Verified step by step guidance

1. Understand that the p-value in a hypothesis test represents the probability of obtaining a test statistic at least as extreme as the observed value, assuming the null hypothesis is true.
2. Recognize that to compute the p-value, you need to know the observed value of the test statistic because it determines the point on the sampling distribution where you evaluate the probability.
3. Identify that the sampling distribution of the test statistic under the null hypothesis is essential because the p-value is calculated based on this distribution.
4. Determine whether the test is one-tailed or two-tailed, as this affects how you calculate the p-value (i.e., which tail(s) of the distribution you consider).
5. Note that the significance level \( \alpha \) is not required to compute the p-value itself; it is used later to decide whether to reject the null hypothesis by comparing it to the p-value.