An English professor surveys a random sample of her students to test whether the average score is greater than 78. Which test is appropriate?

An English professor surveys a random sample of her students to test whether the average score is greater than 78. Which test is appropriate?

• A. 2-sample t-test
• B. 1-sample t-test (degrees of freedom unknown)
• C. Z-test
• D. Paired t-test

Answer: (B)

When you want to determine if a population mean exceeds a fixed value using data from a single sample and you don’t know the population standard deviation, you use a one-sample t-test. Here, you’re testing whether the average score of the students is greater than 78, based on a random sample. Because the population variance is unknown, you estimate it from the sample, and the sampling distribution of the sample mean follows a t-distribution with n−1 degrees of freedom. Since the alternative is that the mean is greater than 78, it’s a one-sided test. The other options don’t fit: a two-sample t-test compares two groups; a paired t-test requires paired observations; a Z-test would require a known population variance (or an extremely large sample), which isn’t indicated here.

When you want to determine if a population mean exceeds a fixed value using data from a single sample and you don’t know the population standard deviation, you use a one-sample t-test. Here, you’re testing whether the average score of the students is greater than 78, based on a random sample. Because the population variance is unknown, you estimate it from the sample, and the sampling distribution of the sample mean follows a t-distribution with n−1 degrees of freedom. Since the alternative is that the mean is greater than 78, it’s a one-sided test. The other options don’t fit: a two-sample t-test compares two groups; a paired t-test requires paired observations; a Z-test would require a known population variance (or an extremely large sample), which isn’t indicated here.