### How does the sampling distribution change when the population parameter varies?

The animation below runs through the sampling distributions expected when samples
of size 20 are draw from a very very large population of varying composition.
These graphics deal with the sampling distribution predicted theoretically.

The **pie chart** on the right represents the population from which numerous
samples are drawn. The proportion of the population that is red
is indicated by the size of the red area--and also by the number appearing above
the pie chart.

The **bar graph** on the left shows the sampling distribution which would
be expected if many many random samples of size 20 were drawn. The numerical
labels on the horizontal axis refer to the number of red units in a random sample.
The height of the column that appears over the label "n" indicates
the probability that a sample contains exactly n red units. For example, when
the fraction of the population that is red amounts to 0.1, the bar over 3 has
height approximately .19 (see the fixed graphic below the animation). This means
that if millions of samples, each of size 20, were to be drawn from a population
that was 10% red, then about 19% of the samples would contain 3 red units.

For your viewing convenience, here is a frame snatched from the animation. This
shows the sampling distribution (of the statistic "number of red units in
a sample of size 20") when the samples are drawn from a population that is
10% red.

This shows the sampling distribution when the population is 50% red.

This page was made September
27, 1998 by Jim Madden, LSU. Updated, November 13, 2002.

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