Topic 9.6 Skills Focus: Selecting an Appropriate Inference Procedure: choose the correct inference procedure (proportion, mean, chi-square, or slope; interval or test; one or two samples; paired or independent) for any scenario across the whole course.

What this topic is asking

The College Board (Topic 9.6) is the course's final skills focus: given any scenario, select the correct inference procedure from the entire toolkit (proportion, mean, chi-square, slope; interval or test; one or two samples; paired or independent), and justify the choice. It integrates Units 6 through 9.

The full decision tree

This is the master map. The first split is categorical versus quantitative versus bivariate-with-a-line. Categorical with two categories uses proportions; categorical with more categories or two variables uses chi-square; one quantitative variable uses means; and a fitted least-squares line with a question about its slope uses regression-slope inference. Slope inference is the new entry this unit adds to the toolkit; its cue is "a least-squares line is fit" and a question about the relationship's slope or existence.

Distinguishing the trickiest pairs

A few boundaries recur on the exam.

• Mean vs slope. A single quantitative variable's average uses a mean procedure; a question about how one quantitative variable changes with another (a fitted line) uses the slope procedure.
• Two-proportion z vs chi-square. A two-category variable across two groups can use either, but more than two categories or several groups needs chi-square.
• Homogeneity vs independence. Several separate samples (homogeneity) versus one sample with two variables (independence), same arithmetic, different design and wording.
• Paired vs independent means. Matched or before/after data are paired (one-sample t on differences); separate groups are two-sample.

Working through the four questions in order resolves all of these before any computation.

Implement and communicate

Each procedure carries its own details: proportion tests use $p_0$ (and pooling for two proportions); mean and slope procedures use $t$ with the right $df$ ($n - 1$ for one mean, $n - 2$ for a slope); chi-square uses expected counts and $\sum (O-E)^2/E$. The conclusion wording must match, "the proportion/mean/slope differs," "the distributions differ," or "the variables are associated", and every answer should respect the scope of inference (random sampling supports generalization; random assignment supports causation) and distinguish statistical significance from practical importance.

Try this

Q1. A study compares mean reaction times for the same subjects under two conditions. Which procedure? [1 point]

• Cue. Paired t-test (matched data; one-sample t on the differences).

Q2. What is the cue that a scenario calls for regression-slope inference rather than a mean procedure? [1 point]

• Cue. A least-squares line is fit and the question concerns how one quantitative variable changes with another (the slope), not a single variable's average.