# t-statistic as opposed to a z-statistic for small test samples

Please help answer the following question.

Why is a t-statistic as opposed to a z-statistic used to test small samples? Does the choice of test statistic alter how you employ the 5-step hypothesis testing procedure?

When testing two populations with small sample sizes, do both sample sizes have to be the same size?

When does the t-statistic approximate the z-statistic? What is the significance of the pictures at the top of the t-statistic table and the z-statistic table

© BrainMass Inc. brainmass.com June 1, 2020, 3:15 pm ad1c9bdddfhttps://brainmass.com/statistics/students-t-test/t-statistic-z-statistic-small-test-samples-47959

#### Solution Preview

1. Why is a t-statistic as opposed to a z-statistic used to test small samples?

When we test a hypothesis of population mean, if we don't know the standard deviation of population, then we fail to use a z-statistic; instead, we can use a t-statistic to do testing.

2. Why is a t-statistic as opposed to a z-statistic used to test small samples? Does the choice of test statistic alter how you employ the 5-step ...

#### Solution Summary

The answers to the following three questions regarding hypothesis testing are provided in detail. The solution is 277 words.