Many textbooks (though not this one) advocate testing the mean of a sample against a hypothesized population mean by using z even if the population standard deviation is not known, so long as the sample size exceeds 30. Those books recommend this because
A) they don't know any better.
B) there are not tables for t for more than 30 degrees of freedom.
C) the difference between t and z is small for that many cases.
D) t and z are exactly the same for that many cases.

Question

Quizplus · Accepted Answer

The recommendation to use z-tests for sample sizes greater than 30, even when the population standard deviation is unknown, is based on the fact that the t-distribution approaches the z-distribution as the sample size increases. For sample sizes larger than 30, the difference between the t and z values becomes negligible, making the z-test a practical approximation.

Many Textbooks (Though Not This One) Advocate Testing the Mean