T Distribution Formula

T distribution formula is used when the sample size is small and the population standard deviation is unknown to us and we want to estimate the mean of the normally distributed population. The T distribution formula is also known as Student’s T Distribution. The curve of the t distribution is almost similar to the normal distribution curve, but the only difference arises that it is a bit short and a little wide than that of the normal distribution curve. Let us study the t distribution formula using solved examples. 

What is T Distribution Formula?

The t distribution formula tells us that the larger the sample size, the more it will be like the normal distribution. For the t distribution formula, we need to know the degree of freedom = m which is nothing but "n-1", where n is the sample size. The t distribution formula for the small sample size is given as:

\( \large \boldsymbol{T Distribution Formula = \frac{\overline{x}-\mu}{\frac{s}{\sqrt{N}}}}  \)

where,

• \(\mu\) is the expected mean value.
• \(\overline{x}\) is the sample mean.
• s is the standard deviation of the sample.
• n is the sample size.

Let's take a quick look at a couple of examples to understand the t-distribution formula better.