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

Quizplus · Accepted Answer

The t-distribution should be used instead of the z-test when the population standard deviation is unknown and estimated by s. The other conditions listed in choices A and C may also be true for using the t-distribution, but they are not sufficient on their own. Choice D is incorrect as there is a valid reason for using the t-distribution in certain cases.

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