Question

What happens to the T distribution as the sample size increases?

Answer 1

T distribution:

T distribution is used to determine normal distribution when the size of the sample is too small to estimate confidence or determine critical values that an observation is a given distance from the mean.

The formula of T distribution is $t=\frac{\overline{x}-\mu }{{\displaystyle \frac{s}{\sqrt{n}}}}$.

Where, $\overline{x}$ is sample mean.

$\mu$ is population mean

$s$ is sample standard deviation.

$n$ is sample size.

The shape of T distribution is affected by the sample size.

If the sample size increase, then T distribution gets closer to the normal distribution.