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Cogito

AP Statistics · Chapter 7 · Lesson 1

Practice Worksheet

Chi-Square Goodness of Fit

Do the counts match the claimed distribution?

12 problems · about 22 minutes · VAR-8.A, DAT-3.M

NameDate

Figure — use these to answer the problems

Observed counts against what the claim predicts. The test measures how far apart they are, category by category.
Category A30
Category B25
Category C20
Category D25
Observed A30
Observed B25
Observed C20
Observed D25
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. 150 observations across 5 equally likely categories. Each expected count?

    Answer

  2. Why is each term divided by the expected count?

    • It scales the gap, so a fixed difference matters more in a small category.
    • To keep the statistic small.

  3. 200 observations across 5 equally likely categories. Each expected count?

    Answer

  4. Six categories. Degrees of freedom?

    Answer

  5. Observed 30, expected 25. What is (observed − expected) squared over expected?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Every expected count must be at least what number?

    Answer

  2. 300 observations, claimed proportion 0.2. Expected count?

    Answer

  3. Should expected counts be rounded to whole numbers? 1 yes, 0 no.

    Answer

Stretch Yourself

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

4 problems

  1. Put the goodness-of-fit procedure in order.

    Write 1 to 4 in the boxes to put these in order.

    • State hypotheses about the claimed distribution.
    • Compute the expected count for each category.
    • Check that all expected counts reach 5.
    • Compute the chi-square statistic and the p-value.

  2. 80 observations across 4 equally likely categories. Each expected count?

    Answer

  3. The Expected Count

    100 observations across 4 equally likely categories. What is each expected count?

    Answer

  4. The Degrees of Freedom

    Four categories in a goodness-of-fit test. Degrees of freedom?

    Answer