Intro Stats · Chapter 9 of 10

Two-Sample and Chi-Square Inference

Compare two groups with two-sample methods and analyze categorical associations and fit with chi-square procedures.

Why this chapter matters

Many real questions involve group comparisons or categorical relationships rather than a single mean or proportion.

What you will learn

  • Apply two-sample confidence intervals and tests for means and proportions.
  • Use chi-square tests for independence and goodness of fit with expected-count checks.
  • Interpret statistically significant differences with careful context language.

Lessons in this chapter

  1. Two-sample means and proportionsChoose and run two-sample procedures based on variable type and design.
  2. Chi-square for independenceEvaluate whether two categorical variables are associated.
  3. Chi-square goodness of fitCompare observed counts to a claimed categorical distribution.
  4. Practical interpretation of group differencesReport direction, size, and uncertainty of detected differences.

Study task

Use a two-way table of study program by pass status to run a chi-square independence test and summarize what the result supports.

Chapter checkpoint

What is the null hypothesis in a chi-square test of independence?

The two categorical variables are independent in the population.