Question

What is the decision to use the Z distribution vs the t distributions as the frequency distributions for hypothesis testing based upon?

Answer 1

Both the Z and the t distributions are used for the hypothesis test for testing the mean values. We use t distribution when the sample size is less than 30 and the population standard deviation is now known. A general rule for selecting which distribution is to be used is that if the population standard deviation is not known, we use the t distribution and when the population standard deviation is known, we use the Z test and hence the standard normal distribution.

Note that for hypothesis test for proportions, we use Z distribution whenever np > 10, n(1-p) > 0 and simple random sampling is done. ( no t distribution is used with hypothesis test for proportions )