t-distribution

statistics This is used to approximate a normal distribution when the sample count is low. Because it’s low sample size, it’s much fatter (more a mound than a peak). Unlike a normal distribution, the shape of it changes slightly depending on the size of the samples ($n$) being used to calculate it.

The t-distribution formula is: $\bar{x}\pm t^{\ast }\frac{s}{\sqrt{n}}$

$t^{\ast }$ can be found by using either a t-table, or by looking up the “inverse t” on the calculator.

Requires:

1. sampled population must be normally distributed
2. samples are selected independently.