# Social Statistics for a Diverse Society

# Chapter Summary

**Chapter 9**

Statistical hypothesis testing is a decision-making process that enables us to determine whether a particular sample result falls within a range that can occur by an acceptable level of chance.The process of statistical hypothesis testing consists of five steps: (1) making assumptions, (2) stating the research and null hypotheses and selecting alpha, (3) selecting a sampling distribution and a test statistic, (4) computing the test statistic, and (5) making a decision and interpreting the results.

Statistical hypothesis testing may involve a comparison between a sample mean and a population mean or a comparison between two sample means.If we know the population variance(s) when testing for differences between means, we can use the *Z *statistic and the normal distribution.However, in practice, we are unlikely to have this information.

When testing for differences between means when the population variance(s) are unknown, we use the *t *statistic and the *t *distribution.

Tests involving differences between proportions follow the same procedure as tests for differences between means when population variances are known.The test statistic is *Z*, and the sampling distribution is approximated by the normal distribution.