Interview question: What is a z test?

In my last post I discussed the t-test, which is a statistical test that can be used on small datasets, and that blog post can be read here:- https://medium.com/@tracyrenee61/interview-question-what-is-a-t-test-c34261aa7a99

In this post I intend to discuss the z-test, which is used to calculate the test statistic for longer datasets. The z-test is a statistical test that is used to determine whether the mean of a sample is significantly different from a known population mean when the population standard deviation is known. It is particularly useful when the sample size is large, being greater than 30 elements in the sample.

The z-test can also be defined as a statistical method that is used to determine whether the distribution of the test statistics can be approximated using the normal distribution or not. It is the method to determine whether two sample means are approximately the same or different when their variance is known and the sample size is large.

The z-test compares the difference between the sample mean and the population means by considering the standard deviation of the sampling distribution. The resulting Z-score represents the number of standard deviations that the sample mean deviates from the population mean. This Z-Score is also known as Z-Statistics, and can be formulated as:-