#### LoveStruck16

##### New member
K the question is...

- What is the decision to use the unit normal (i.e. Z) distribution versus the student's T distributions as the frequency distribution for hypothesis testing based upon?

If T is a statistic that is approximately normally distributed under the null hypothesis, the next step in performing a Z-test is to determine the expected value ? of T under the null hypothesis, and then obtain an estimate s of the standard deviation of T. We then calculate the standard score Z = (T ? ?) / s, from which one-tailed and two-tailed p-values can be calculated as ?(?|Z|) and 2?(?|Z|), respectively, where ? is the standard normal cumulative distribution function.

thanks.

#### galactus

##### Super Moderator
Staff member
Noramlly, the t is used when the sample size is less than 30. That is one criterion.

As the sample size gets larger, the t approaches the z.