Hypothesis Tests: One Sample Response Variable Categorical Quantitative Population Parameter Sample Estimate Inferential Procedure one-proportion Z one-sample t Test statistic Chapter 12 13 P-value Z table T table with df = (n – 1) because σ is unknown

Hypothesis Tests: Two independent samples Response Variable Categorical Quantitative Population Parameter Sample Estimate Inferential Procedure two-proportion Z two-sample t Test statistic Chapter 12 13 P-value Z table T table with df = min{(n1–1), (n2–1)} because σ1 and σ2 are unknown

What can go wrong: Two types of errors This comes from Section 12.1. Generally speaking: • A type I error occurs when you erroneously reject H0. • A type II error occurs when you erroneously fail to reject H0. The power of a test is the probability, given a particular alternative is true, of rejecting H0. The level of significance is the p-value cutoff for rejecting H0. (Often it’s 0.05.) If H0 is true, the level of significance is the probability of a type I error.

Relationship between tests and CIs If a 95% CI contains the null value… …we fail to reject H0 at the 0.05 level for a 2-sided test. If a 95% CI does not contain the null value… …we reject H0 at the 0.05 level for a 2-sided test.

Population version of regression (ith individual) The value εi is called the deviation. We assume that it is normal with mean 0 and standard deviation σ. Sample version of regression (ith individual) The value ei is called the residual. The standard deviation of all the ei can be used to estimate σ.