What does the t test for independent samples assess?

What does the t test for independent samples assess?

• A. Whether the means of two independent populations are equal.
• B. Whether the means of two related populations are equal.
• C. Whether the variances of two populations are equal.
• D. Whether a sample mean equals the population mean.

Answer: (A)

The main idea this test examines is whether the average outcome differs between two independent groups. It asks if the population means of those groups are equal by testing the null hypothesis that mu1 equals mu2. The t statistic is built from the difference between the two sample means, scaled by the standard error that reflects sample sizes and variability, and a p-value indicates how likely this difference would be if the true means were the same. If the result is statistically significant, we infer a difference in the population means. This differs from related-samples tests, which compare paired or matched observations within the same subjects. It also isn’t about whether variances are equal—that concern is handled separately (and the t-test can use either equal- or unequal-variance versions). And it isn’t about a single sample mean versus a population mean, which is a one-sample t-test.

The main idea this test examines is whether the average outcome differs between two independent groups. It asks if the population means of those groups are equal by testing the null hypothesis that mu1 equals mu2. The t statistic is built from the difference between the two sample means, scaled by the standard error that reflects sample sizes and variability, and a p-value indicates how likely this difference would be if the true means were the same. If the result is statistically significant, we infer a difference in the population means.

This differs from related-samples tests, which compare paired or matched observations within the same subjects. It also isn’t about whether variances are equal—that concern is handled separately (and the t-test can use either equal- or unequal-variance versions). And it isn’t about a single sample mean versus a population mean, which is a one-sample t-test.