1. Review of Hypothesis Testing

2. Types of Tests 1-Sample z 1-Sample t 2-Sample t 1-Proportion
Paired t-test
Chi-Square G.O.F test
Chi-Square Test of Independence
Linear Regression t-test

3. Universal Conditions
Randomization Condition: The sample should be a simple random sample of the population.
10% Condition: (Independence) If sampling has not been made with replacement, and you are drawing from a finite population then the sample size, n, must be no larger than 10% of the population.

4. 1-Sample-Z Test Quantitative Data
You know (sigma) the standard deviation of the population.
Normality Check: Stated in the question, probability plot, n is at least 30.

5. 1-Sample t-test Quantitative Data
You do not know (sigma) the standard deviation of the population.
You use “s” the standard deviation of the sample to approximate sigma.
Normality Check: (Central Limit Theorem) Sample Size of at least 30

6. 2-Sample t-test 2 Sets of Quantitative Data
You do not know (sigma) the standard deviation of either population.
You use s1 and s2 to approximate sigma for both populations.
Normality Check: (CLT) Both sample sizes are at least 30.

7. 1-Proportion (Categorical Data) Qualitative Data
You use p-hat and q-hat to approximate the standard deviation of the population.
Normality Check: The sample size has to be big enough so that both np and nq are at least 10.

8. 2-Proportion 2 Sets of (Categorical Data) Qualitative Data
You use p-hat and q-hat to approximate the standard deviation for both populations.
Success/Failure Condition: The sample size has to be big enough so that both n1p1, n1q1 n2p2, n2p2 are at least 10.

9. Paired t-test Quantitative Data
Same as a one sample t-test but you have two pieces of data for each subject or experimental unit.
Usually (Pre-Test/Post-Test)
Normality Check: (CLT) “n” is at least 30

10. Chi-Square Goodness of Fit
When you are comparing multiple proportions for a distribution. (M & M project)
Conditions:
No expected counts less than 5.
All variables are independent.
Expected Counts equal sample size multiplied by the %’s stated in the model.

11. Chi-Square Test of Independence
When you are comparing two categorical variables. (Two Way Table)
Conditions:
No expected counts less than 5.
All values are independent.
The expected count in any cell of a two-way table when H0 is true is
Finding Expected Counts

12. Linear Regression t-test
Conditions for Regression Inference
Suppose we have n observations on an explanatory variable x and a response variable y. Our goal is to study or predict the behavior of y for given values of x.
• Linear The (true) relationship between x and y is linear. For any fixed value of x, the mean response µy falls on the population (true) regression line µy= α + βx. The slope b and intercept a are usually unknown parameters.
• Independent Individual observations are independent of each other.
• Normal For any fixed value of x, the response y varies according to a Normal distribution.
• Equal variance The standard deviation of y (call it σ) is the same for all values of x. The common standard deviation σ is usually an unknown parameter.
• Random The data come from a well-designed random sample or randomized experiment.