# The difference between t-tests and z-tests

In drawing an inference using a single mean in hypothesis testing, you often have a choice between doing a z-test or a t-test. Many researchers will always choose to do the t-test even under circumstances where the z-test would work as well. Explain why the t-test was developed and why it is preferred.

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#### Solution Preview

The t-test was developed to test hypotheses when we're dealing with samples that have fewer than approximately 30 people/scores. When we have too few scores, the shape of the sampling distribution of means (i.e. the distribution of the means of many samples) is not normally distributed. Since the z-test assumes normality (by ...

#### Solution Summary

This solution explains the difference in assumptions of a one-sample t-test and a z-test. It further explains why researchers may prefer to use the t-test in analyses that could use a z-test.