T-test – a parametric hypothesis test

In the last chapter, the z-test for means was applied when population standard deviations were known. However, in the real world, it is not easy (or virtually impossible) to obtain the population standard deviation. In this section, we will discuss another hypothesis test called the t-test, which is used when the population standard deviations are unknown. The mean and the standard deviation of a population are estimated by taking the mean and the standard deviation of sample data representative of this population.

Broadly speaking, the method for the t-test for means is very similar to the one for the z-test for means, but the calculations for the test statistic and p-value are not the same as for the z-test. The test statistic is computed by the following formula:

t =   _ x  − μ _ s/ √ _ n  

Here,  _ x  , μ, s, and n are the sample mean...