## Two Populations -- an introduction

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:
1. Two Populations; Two Independent Samples, σ's known
1. Confidence Interval for the difference between means
2. Hypothesis Test for the difference between means
2. Two Populations; two independent samples, σ's unknown
1. Confidence Interval for the difference between means
2. Hypothesis Test for the difference between means
3. One Population; Paired Samples
1. Confidence Interval for the difference between means
2. Hypothesis Test for the difference between means
4. Two Populations; Proportions
1. Confidence Interval for the difference between proportions
2. Hypothesis Test for the difference between proportions
5. Two Populations; Independent Samples -- Standard Deviation
1. The F-distribution
2. Confidence Interval for the ratio of standard deviations
3. Hypothesis Test for the ratio of standard deviations