In the context of performing hypothesis tests about means, the t-test is principally a test of which parameter?

• A. The correlation coefficient $\rho$ between two variables
• B. A population proportion (or the difference between two population proportions)
• C. The population variance ${\sigma }^2$
• D. A population mean (or the difference between two population means) when the population standard deviation is unknown

Answer: (D)

Verified step by step guidance

1. Understand that the t-test is used primarily when we want to make inferences about a population mean, especially when the population standard deviation is unknown.
2. Recall that the t-test compares the sample mean to a hypothesized population mean to determine if there is a statistically significant difference.
3. Recognize that the t-test is not designed to test parameters like the correlation coefficient (\(\rho\)), population proportion, or population variance (\(\sigma\)^{2}).
4. Note that the t-test uses the sample standard deviation as an estimate for the unknown population standard deviation, which is why the t-distribution (rather than the normal distribution) is used.
5. Conclude that the parameter tested by the t-test is the population mean (or the difference between two population means) under the condition that the population standard deviation is unknown.