## Two Populations -- an introduction

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Up to this point we have been looking at
populations and samples,
but in each instance we have been looking
at one sample from a single population.
There are really only two things that we have been
doing: finding a confidence interval for a
population parameter (the mean, the proportion, or the standard deviation)
and testing a hypothesis about a population parameter
(again, the mean, the proportion, or the standard
deviation).
The next number of topics expand that view to looking at
two samples,
usually from two populations.
We will do the same thing in this new
situation, find confidence intervals and formulate
hypothesis tests.

The good news is that the ideas and methods
of the earlier topics carry forward to this
new situation. The bad news is that the
computations get a bit more intense. Of course
we have R to help mitigate those
more complex computations.

The subsequent web pages will walk us through different
situations. Rather than go through these twice,
once for developing confidence intervals
and once for developing hypothesis tests, we will
do both of those in each of the following
situations:
- Two Populations; Two Independent Samples, σ's known
- Confidence Interval for the difference between means
- Hypothesis Test for the difference between means

- Two Populations; two independent samples, σ's unknown
- Confidence Interval for the difference between means
- Hypothesis Test for the difference between means

- One Population; Paired Samples
- Confidence Interval for the difference between means
- Hypothesis Test for the difference between means

- Two Populations; Proportions
- Confidence Interval for the difference between proportions
- Hypothesis Test for the difference between proportions

- Two Populations; Independent Samples -- Standard Deviation
- The F-distribution
- Confidence Interval for the ratio of standard deviations
- Hypothesis Test for the ratio of standard deviations

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©Roger M. Palay
Saline, MI 48176 Febbruary, 2016