Introducing the central limit theorem used in t-distribution

The CLT says that the distribution from the sum (or average) of many independent and identically distributed random variables would jointly form a normal distribution, regardless of the underlying distribution of these individual variables. Due to the CLT, normal distribution is often used to approximate the sampling distribution of various statistics, such as the sample mean and the sample proportion.

The t-distribution is related to the CLT in the context of statistical inference. When we’re estimating a population mean from a sample, we often have no access to the true standard deviation of the population. Instead, we resort to the sample standard deviation as an estimate. In this case, the sampling distribution of the sample mean doesn’t follow a normal distribution, but rather a t-distribution. In other words, when we extract the sample mean from a set of observed samples, and we are unsure of the population...