1. 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

2. 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

3. 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.

4. 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.

5. 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.