A flower pot manufacturer samples 25 pots to test whether mean thickness differs from 4 mm, with sample mean 4.3 mm. Which test should be used?

A flower pot manufacturer samples 25 pots to test whether mean thickness differs from 4 mm, with sample mean 4.3 mm. Which test should be used?

• A. One-sample t-test with 24 degrees of freedom
• B. Two-sample t-test
• C. Z-test for a single mean
• D. Paired t-test

Answer: (A)

Testing whether a single population mean is different from a specified value when the population standard deviation is unknown. With 25 pots, you’re comparing the sample mean thickness to the hypothesized mean of 4 mm. Because sigma is unknown and the sample size isn’t extremely large, the appropriate method is the one-sample t-test. It uses the sample standard deviation and follows a t distribution with n minus one degrees of freedom, which is 24 here. The test checks whether the observed average thickness 4.3 mm differs from 4 mm in a two-sided way. The other options don’t fit: a two-sample t-test compares two independent groups; a Z-test for a single mean requires known sigma or a very large sample; a paired t-test is for matched or repeated measurements. So the correct approach is a one-sample t-test with 24 degrees of freedom.

Testing whether a single population mean is different from a specified value when the population standard deviation is unknown. With 25 pots, you’re comparing the sample mean thickness to the hypothesized mean of 4 mm. Because sigma is unknown and the sample size isn’t extremely large, the appropriate method is the one-sample t-test. It uses the sample standard deviation and follows a t distribution with n minus one degrees of freedom, which is 24 here. The test checks whether the observed average thickness 4.3 mm differs from 4 mm in a two-sided way. The other options don’t fit: a two-sample t-test compares two independent groups; a Z-test for a single mean requires known sigma or a very large sample; a paired t-test is for matched or repeated measurements. So the correct approach is a one-sample t-test with 24 degrees of freedom.