Question 1
A researcher took independent random samples of 100 adults from each of two cities and compared the distributions of preferred way to exercise (gym, outdoors, home). Which test is appropriate?
Which inference procedure? A guide for AP Statistics
Ask three questions: is the variable categorical or quantitative, how many groups are there, and are the data paired?
| One proportion | one-sample z interval or test |
|---|---|
| Two proportions | two-sample z interval or test (pool only in the test) |
| One mean or paired data | one-sample t on the values or the differences |
| Two independent means | two-sample t |
| Two-way table | chi-square test for homogeneity or independence |
Categorical or quantitative?
Counts of yes and no lead to proportions and chi-square. Measurements lead to means and t procedures.
Paired or independent?
Two measurements on the same people, objects or matched pairs are paired: analyze the differences with a one-sample t procedure. Separate groups are independent: use a two-sample procedure.
Homogeneity or independence?
Several separate samples compared on one variable: homogeneity. One sample classified by two variables: independence. The arithmetic is the same; the design decides the name and the conclusion.
Try 2 questions
Question 2
Which study calls for a two-sample t procedure rather than a paired t procedure?
Next step
Questions people ask
When do you use t instead of z in AP Statistics?
For means, whenever the population standard deviation is estimated by the sample standard deviation, which is almost always. Proportions use z.
What is the difference between homogeneity and independence?
Homogeneity compares several populations from separate samples; independence checks for an association between two variables in one sample.