# Chapter Main Points and Learning Objectives

Chapter main points

• 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.

Learning objectives

1. Describe the assumptions of statistical hypothesis testing
2. Define and apply the components in hypothesis testing
3. Explain what it means to reject or fail to reject a null hypothesis
4. Calculate and interpret a test for two sample cases with means or proportions
5. Determine the significance of t-test and Z-test statistics