why do we always use the standard normal distribution Z when

why do we always use the standard normal distribution (Z) when calculating a sample size?

Solution

The reason is that t-critical values vary with sample size which we do not know beforehand when we are calculating the sample size for desired margin of error and confidence level. Therefore, we use z instead of t, assuming that the sample size will be large enough that the t-values would approximately be equal to z-values.