What's the difference between a z test and a t test?

Question

What do both require, and why do we rarely use z tests?

Answer 1

A z-test and a t-test are both statistical methods used to test hypotheses about population means, but they differ in their assumptions and applications. A z-test is used when the population standard deviation is known, and the sample size is large (typically n>30), as it assumes that the sampling distribution of the mean follows a normal distribution. In contrast, a t-test is used when the population standard deviation is unknown, and the sample size is small (n≤30), relying on the t-distribution to account for additional variability due to estimating the standard deviation from the sample. The t-distribution is slightly broader and more variable than the normal distribution, particularly for smaller sample sizes, to reflect the increased uncertainty in the estimate of the population standard deviation. As the sample size increases, the t-distribution approaches the normal distribution, making the z-test and t-test results converge in large samples. I hope you found this to be helpful. If you had any additional question, please let me know. Take care,

Dr. Christal-Joy Turner

Answer 2

Z tests are used when we know the population standard deviation and you have a sample larger than 30. In real-life experiments, you will rarely ever know the population standard deviation. Instead, we use a t-test, which uses the standard error of the mean. The samples in t-tests tend to be smaller, so it's important to account for the difference between the population and sample mean.