When is a t-test used to test a population mean, rather than a z-test?

When the sample is very large and

\sigma

is known exactlyCorrect answerYour answerWhen the data are categories rather than numbersCorrect answerYour answerWhen the sample is small and

\sigma

is unknownCorrect answerYour answerOnly when the sample mean equals the claimed meanCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

The t-test uses the sample standard deviation $s$ in place of the unknown $\sigma$ .
That matters most for a small sample, which is where the t-distribution is needed.

Worth noting

With a large sample and $\sigma$ known, the normal z-test is used.

Ten questions from Sampling, Inference & the t-Test, at your own pace.

Explanation