A random sample of size n has been selected from a normally distributed population whose standard deviation is s. In estimating an interval for the population mean, the t-distribution should be used instead of the z-test if:
A) n ?
30 and $\sigma$ is known.
B) $\sigma$ is unknown and estimated by s, and the population is normal.
C) Population is normal and $\sigma$ is known.
D) None of these choices are correct.

Question

A random sample of size n has been selected from a normally distributed population whose standard deviation is s. In estimating an interval for the population mean, the t-distribution should be used instead of the z-test if:
A) n ?
 30 and $\sigma$ is known.
B) $\sigma$ is unknown and estimated by s, and the population is normal.
C) Population is normal and $\sigma$ is known.
D) None of these choices are correct.

Quizplus · Accepted Answer

The t-distribution should be used instead of the z-test when the population standard deviation is unknown and estimated by the sample standard deviation (s), which is the case in choice B. When the population standard deviation is known, the z-test can be used. When the sample size is large (greater than 30), both the z-test and t-distribution can be used as they converge to the same value.

A Random Sample of Size N Has Been Selected from a Normally