3/18/2026

Hypothesis Testing

• One variance
• Two variances
• More than two variances

Neyman-Pearson Lemma

• Proof and examples provided in class materials folder - see Chapter 10 - NP.pdf

Likelihood ratio tests - see Chapter 10 - Likelihood ratio tests.pdf

• Nuisance parameters
• Vector of all parameters
• Parameter space
• Setting up the hypotheses
• Maximize the likelihood function under H0
• Maximize the likelihood function under H1
• Form the ratio
• Identify the rejection region

Class Activity

• What is the power of a test?
• Provide at least one example of how to compute power, preferrably with RStudio.

Problem Session

• Chapter 10 Exercises 43, 49, 51, 59, 65, 73, 77, 88, 93, 95, 99, and 101

We will have a Problem Session (covering through Section 10.9) on Friday.