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Cogito

AP Statistics · Chapter 3 · Lesson 3

Practice Worksheet

Comparing Two Proportions

Is the difference bigger than chance?

12 problems · about 22 minutes · UNC-4.C, DAT-3.D

NameDate

Figure — use these to answer the problems

Two groups of different sizes. Compare the proportions rather than the raw counts.
Group 130
Group 245
Group 1 successes30
Group 2 successes45
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. An interval for p₁ − p₂ runs from 0.05 to 0.21. Is a difference established? 1 yes, 0 no.

    Answer

  2. Why does a two-proportion test pool the samples?

    • The null assumes the proportions are equal, so one estimate is best.
    • To get a larger sample size.

  3. Sample proportions 0.7 and 0.5. Difference?

    Answer

  4. An interval runs from 0.03 to 0.19. Does it contain zero? 1 yes, 0 no.

    Answer

  5. That interval establishes a difference? 1 yes, 0 no.

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. How many success and failure counts must be checked for two groups?

    Answer

  2. Do you pool for a significance test? 1 yes, 0 no.

    Answer

  3. Do you pool for a confidence interval? 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 procedure by whether it pools the samples.

    Write each item under the heading it belongs to: Two-proportion significance test · A procedure that assumes the proportions are equal · Two-proportion confidence interval · A procedure making no equality assumption

    Pools

    Does not pool

  2. Sample proportions 0.4 and 0.55. Difference?

    Answer

  3. The Interval

    An interval for p₁ − p₂ runs from −0.02 to 0.14. Does it contain zero? 1 yes, 0 no.

    Answer

  4. The Difference

    Sample proportions 0.6 and 0.45. What is the difference?

    Answer