# 9: Inferences with Two Samples

You have learned to conduct hypothesis tests on single means and single proportions. You will expand upon that in this chapter. You will compare two means or two proportions to each other. The general procedure is still the same, just expanded. To compare two means or two proportions, you work with two groups. The groups are classified either as independent or matched pairs. Independent groups consist of two samples that are independent, that is, sample values selected from one population are not related in any way to sample values selected from the other population. Matched pairs consist of two samples that are dependent. The parameter tested using matched pairs is the population mean. The parameters tested using independent groups are either population means or population proportions.

• 9.1: Prelude to Hypothesis Testing with Two Samples
This chapter deals with the following hypothesis tests: Independent groups (samples are independent) Test of two population means. Test of two population proportions. Matched or paired samples (samples are dependent) Test of the two population proportions by testing one population mean of differences.
• 9.2: Inferences for Two Population Means- Large, Independent Samples
Suppose we wish to compare the means of two distinct populations. Our goal is to use the information in the samples to estimate the difference in the means of the two populations and to make statistically valid inferences about it.
• 9.3: Inferences for Two Population Means - Unknown Standard Deviations
When one or the other of the sample sizes is small, as is often the case in practice, the Central Limit Theorem does not apply. We must then impose conditions on the population to give statistical validity to the test procedure. We will assume that both populations from which the samples are taken have a normal probability distribution and that their standard deviations are equal.
• 9.4: Inferences for Two Population Means - Paired Samples
A confidence interval for the difference in two population means using paired sampling is computed using a formula in the same fashion as was done for a single population mean. The same five-step procedure used to test hypotheses concerning a single population mean is used to test hypotheses concerning the difference between two population means using pair sampling. The only difference is in the formula for the standardized test statistic.
• 9.5: Inferences for Two Population Proportions
A confidence interval for the difference in two population proportions is computed using a formula in the same fashion as was done for a single population mean. The same five-step procedure used to test hypotheses concerning a single population proportion is used to test hypotheses concerning the difference between two population proportions. The only difference is in the formula for the standardized test statistic.
• 9.6: Which Analysis Should You Conduct?
• 9.E: Hypothesis Testing with Two Samples (Optional Exercises)
These are homework exercises to accompany the Textmap created for "Introductory Statistics" by OpenStax.