Which option correctly describes when a one-sample t-test is used?

Which option correctly describes when a one-sample t-test is used?

• A. To compare two independent sample means.
• B. To compare a sample mean to a known population mean when the population standard deviation is known.
• C. To compare a sample mean to a hypothesized population mean when the population standard deviation is unknown.
• D. To assess correlation between two variables.

Answer: (C)

Use a one-sample t-test when you have a single sample and you want to test whether its mean differs from a hypothesized population mean, and you don’t know the population standard deviation. Because sigma is unknown, you estimate it with the sample standard deviation and base the test on the t distribution, with degrees of freedom equal to n minus 1. The test statistic is t = (x̄ − μ0) / (s/√n), which captures the extra uncertainty from estimating sigma. If the population standard deviation were known, you’d use a z-test instead of a t-test. The other scenarios describe different analyses: comparing two independent means is a two-sample comparison, and assessing correlation involves a relationship between two variables, not a mean against a fixed value.

Use a one-sample t-test when you have a single sample and you want to test whether its mean differs from a hypothesized population mean, and you don’t know the population standard deviation. Because sigma is unknown, you estimate it with the sample standard deviation and base the test on the t distribution, with degrees of freedom equal to n minus 1. The test statistic is t = (x̄ − μ0) / (s/√n), which captures the extra uncertainty from estimating sigma. If the population standard deviation were known, you’d use a z-test instead of a t-test. The other scenarios describe different analyses: comparing two independent means is a two-sample comparison, and assessing correlation involves a relationship between two variables, not a mean against a fixed value.