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Comparing the Normal and Student t Distributions
On the previous page we noted that there seemed to be more extreme values
in the sampling distribution of t than for the
sampling distribution of z. Mathematical statisticians
have derived the formula for the sampling distribution of t,
the distribution that would result if on the previous page we were able to
sample an infinite number of times. The graph below allows you to compare
the sampling distribution of t (in blue) with
the sampling distribution of z (in red). Unlike
the normal distribution of means when the variance is known, the
Student-t distribution of means depends on the number of observations on
which the mean is based. When this
page first loads, the graph compares the normal distribution with the
Student t-distribution for the example of the previous page in which
the mean is based on five observations.
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Use the scrollbar on the right to change the "degrees of
freedom" for the t-distribution.
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The one parameter in the Student t-distribution reflects the number of
observations on which the mean is based. This parameter is the "degrees
of freedom," often represented as df. When asking
questions of a single mean, df = n - 1. So, when the mean is based on
five observations, df = 5 - 1 = 4.
Be sure to observe what happens to the comparison as the number of
observations and, hence, the degrees of freedom increase.
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© 1999, Duxbury Press.
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