Student's T-Distrubtion

The Student's T-distrubution is a symmetrical distribution that is largely used to make inferences regarding the mean of a normal distribution whose variance is unnkown or when working with a small sample size.

The t-distrubtion is less peaked and has fatter tails than a standard normal distrubiton. This makes it a more conservative measure for constructing confidence intervals for the population mean.

Properties

The student's T-distrubtion is

• symmetrical and centered about 0
• defined by one parameter, the degrees of freedom (df). The degrees of freedome are equal to one less than the number of sample observations, n-1, for sample means
• less peaked than a normal distrubtion with more probability in the tails
• dynamic. As the sample size and degrees of freedom increase, the shape of the t=distrubtion approaches a standard normal distrubtion.

Thicker Tails

The t-distrubtion has thicker tails relative to the z-distribution. This is important in hypothesis testing because the thicker tails mean more observations outside the center of the distribution. In hypothesis testing using the t-distribution it is more difficult to reject the null than in hypothesis tesing using the z-distribution.