Q#23: Difference between t-test and z-test

Explain the differences between two statistical tests called t-tests and z-tests.

In your explanation, create two examples of when you would use the tests, one scenario for t-tests and one scenario for z-tests. This will help highlight real life situations when one test would be utilized over the other.
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ANSWER

This question tests your understanding of statistics, specifically statistical tests.

Both t-tests and z-tests are univariate hypothesis tests, meaning that they test one independent variable against a binary result, either it has an effect or it doesn’t. The main difference is that of the distribution your hypothesis is tested against, a t-test uses a non-parametric distribution where the mean is known and the variance is estimated from the sample, whereas the z-test uses a standard normal distribution, with centered mean and unit standard deviations. To read in depth: Difference Between t-test and z-test (with Comparison Chart) — Key Differences

An example of when to use the z-test could be in the evaluation of a classes performance on a standardized exam. To evaluate if class A as a whole performed better than average. Here a z-test works because the distribution of standardized exam scores is normal and the binary outcomes is that class A did perform better than normal or it did not.

An example of a t-test can simply be any scientific experiment, such as the effect of a drug vs a control group. The compared distribution is represented by the performance of the control group and the binary outcome is that the drug has an effect on performance or it does not.