In a one-sample t-test, which distribution is used to determine critical values?

In a one-sample t-test, which distribution is used to determine critical values?

• A. Standard normal distribution.
• B. F distribution.
• C. t distribution with n minus 1 degrees of freedom.
• D. Chi-square distribution.

Answer: (C)

When you conduct a one-sample t-test, the population standard deviation is unknown and you estimate it with the sample standard deviation. This introduces extra variability into the test statistic, so the distribution that governs (X̄ − μ0) / (s/√n) under the null is the t distribution with n − 1 degrees of freedom. The t distribution’s heavier tails reflect that uncertainty, and it approaches the standard normal as the sample size grows. The standard normal distribution would apply only if sigma were known. The F distribution is used for comparing variances or in ANOVA-type tests, and the chi-square distribution is tied to variance estimates in other contexts. Thus, the t distribution with n − 1 degrees of freedom is the appropriate source of critical values here.

When you conduct a one-sample t-test, the population standard deviation is unknown and you estimate it with the sample standard deviation. This introduces extra variability into the test statistic, so the distribution that governs (X̄ − μ0) / (s/√n) under the null is the t distribution with n − 1 degrees of freedom. The t distribution’s heavier tails reflect that uncertainty, and it approaches the standard normal as the sample size grows.

The standard normal distribution would apply only if sigma were known. The F distribution is used for comparing variances or in ANOVA-type tests, and the chi-square distribution is tied to variance estimates in other contexts. Thus, the t distribution with n − 1 degrees of freedom is the appropriate source of critical values here.