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Cogito

AP Statistics · Chapter 7 · Lesson 2

Practice Worksheet

Chi-Square for Two-Way Tables

Independence and homogeneity.

12 problems · about 22 minutes · VAR-8.E, DAT-3.O

NameDate

Figure — use these to answer the problems

Two groups compared on one variable. Convert to proportions before judging whether they differ.
Group 1 yes30
Group 1 no20
Group 2 yes20
Group 2 no30
Group 1 yes30
Group 1 no20
Group 2 yes20
Group 2 no30
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. A 2 by 5 table. What are the degrees of freedom?

    Answer

  2. What distinguishes independence from homogeneity?

    • How the data was collected: one sample or several.
    • The formula used.

  3. A 2 by 2 table. Degrees of freedom?

    Answer

  4. A 4 by 5 table. Degrees of freedom?

    Answer

  5. Row total 40, column total 50, grand total 200. Expected count?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. One sample classified by two variables. Which test? 1 independence, 2 homogeneity.

    Answer

  2. Several separate samples compared on one variable. Which test? 1 or 2?

    Answer

  3. Does the arithmetic differ between the two tests? 1 yes, 0 no.

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Sort each study by which chi-square test it needs.

    Write each item under the heading it belongs to: One survey recording two characteristics per person · A single sample cross-classified · Three separate schools surveyed and compared · Separate random samples from two populations

    Independence

    Homogeneity

  2. A 3 by 3 table. Degrees of freedom?

    Answer

  3. The Expected Count

    Row total 50, column total 60, grand total 200. What is the expected count?

    Answer

  4. The Degrees of Freedom

    A 3 by 4 table. What are the degrees of freedom?

    Answer