Which of the following is not one of the steps in conducting a one-sample $t$-test?

• A. Decide whether to reject or fail to reject the null hypothesis based on the $p$-value.
• B. Calculate the test statistic using the sample data.
• C. Determine the population variance exactly.
• D. State the null and alternative hypotheses.

Answer: (C)

Verified step by step guidance

1. Understand the purpose of a one-sample t-test: it is used to compare the sample mean to a known or hypothesized population mean when the population variance is unknown.
2. Recall the typical steps in conducting a one-sample t-test: first, state the null hypothesis (\(H_0\)) and the alternative hypothesis (\(H_a\)).
3. Next, calculate the test statistic using the formula \(t = \frac{\bar{x} - \mu_0}{s / \sqrt{n}}\), where \(\bar{x}\) is the sample mean, \(\mu_0\) is the hypothesized population mean, \(s\) is the sample standard deviation, and \(n\) is the sample size.
4. Then, determine the p-value associated with the calculated t-statistic and the degrees of freedom (\(df = n - 1\)).
5. Finally, decide whether to reject or fail to reject the null hypothesis based on the p-value and the chosen significance level (\(\alpha\)). Note that determining the population variance exactly is not a step in the one-sample t-test because the population variance is unknown and estimated from the sample.