### Math 225 Course Notes

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### Chapter 5

#### Contents

When a random sample is taken,
a statistic (such as the sample mean)
is a random variable
since it might take on different values if the sample were taken again.
The distribution of this statistic is called its
sampling distribution.
Every sampling distribution can be summarized by its
mean and
standard deviation.
The standard deviation of a sampling distribution is called
the *standard error* of the statistic,
and may usually be interpreted as
a typical distance for the statistic to vary from its mean.

When samples are sufficiently large,
the shape of the sampling distribution is approximately normal,
by the
central limit theorem.

We will consider four different sampling distributions in this chapter:
the sample mean from a single population,
the difference between two sample means from
two independent samples,
the sample proportion from a single population,
and the difference between two sample proportions
from two independent samples.

The logic in all of these cases is the same.
The methodology for solving problems is also the same,
except that different settings require the use of different formulas
for the mean and standard error.

Last modified: Feb 7, 1996

Bret Larget,
larget@mathcs.duq.edu