Describe when a ztest should be performed as opposed to a tt

Describe when a z-test should be performed as opposed to a t-test? Which (if any) can we use all the time? Why or why not?

Solution

Describe when a z-test should be performed as opposed to a t-test? Which (if any) can we use all the time? Why or why not?

A z test needs to know the population standard deviation, and an underlying normal distribution. However, if the sample size we have is large enough (say, n > 30), then many people would treat the sampling distirbution of means to be approximately normal already. But that\'s just \"approximately\".

The t test does not need to know the population standard deviation, nor does it need an underlying normal distirbution. It makes up for what we don\'t know about the population.

Hence, we can use the t-test all the time, but not z test.