The third major topic in statistical theory is hypothesis testing. This topic starts with crafting the hypotheses and continues with calculating p-values. Much-maligned, p-values are a measure of how well the data support your null hypotheses. Calculating p-values fundamentally depends on the distribution of the test statistic. In the Normal case, these distributions are easily determined from MATH 321 work.

How do we determine the distribution of the test statistics? How do we formulate test statistics so that their distribution is easily determined? What do we do when the distribution of the test statistics is unknown, like when we do not know the distribution of the variables?

Objectives

By the end of this module, the student will

• create alternative hypotheses and null hypotheses, both simple and composite
• use the Neyman-Pearson Lemma
• formulate an appropriate likelihood-ratio test
• determine if a test is uniformly most powerful (UMP)
• perform tests of single-parameter hypotheses
• perform tests comparing two parameters

Readings

All readings are from our official textbook.

• Sections 6.1 to 6.5
• Guided Thought Questions

Example Scripts

The following R script provide some additional practice in statistical computing. Consider these to be required activities.

• Power Curves

Statistical Computing Activity

• SCA 3: Skewness Testing

Assignment

• Assignment 3