t Distribution
Prerequisites
Normal
Distribution, Areas
Under Normal Distributions, Degrees of Freedom,
Confidence Interval for the Mean
Learning Objectives
 State the difference between the shape of the t and normal distribution
 State how the difference between the shape of the t and normal distribution
is affected by the degrees of freedom
 Use a t table to find the value of t to use in a confidence interval
 Use the t calculator to find the value of t to use in a confidence
interval
The t distribution is very similar to the normal
distribution when the estimate of variance
is based on many degrees
of freedom but has relatively more scores in its
tails when there are fewer degrees of freedom. The normal distribution
has relatively more scores in the center of the distribution
and the t distribution has relatively more in the tails. The
t distribution is therefore
leptokurtic
Since the t distribution is leptokurtic, the percentage of the
distribution within 1.96 standard deviations of the mean is less
than the 95% for the normal distribution. Table 1 shows the number
of standard deviations from the mean required to contain 95% and
99% of the area of the t distribution for various numbers of degrees
of freedom. These are the values of t that you use in a confidence
interval. The corresponding values for the normal distribution
are 1.96 and 2.58 respectively. Notice that with few degrees of
freedom, the values of t are much higher than the corresponding
values for a normal distribution and that the difference decreases
as the degrees of freedom increase. The values in Table 1 can be
obtained from the "Find
t for a confidence interval" calculator.
Online:
Calculator: Find t for a confidence interval
Online:
Calculator: t distribution
