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Cogito

AP Statistics · Chapter 6 · Lesson 3

Practice Worksheet

Errors and Power

The two ways a test can be wrong.

12 problems · about 21 minutes · UNC-5.A, UNC-5.C

NameDate

Figure — use these to answer the problems

Observed against expected. The larger the gap, the more power a test has to detect it.
Observed62
Expected50
Observed62
Expected under the null50
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. The Type II error rate is 0.25. What is the power?

    Answer

  2. Which change improves both error rates at once?

    • A larger sample size.
    • A smaller significance level.

  3. Failing to reject a false null. Which error? 1 Type I, 2 Type II.

    Answer

  4. Alpha is 0.05. What is the Type I error rate?

    Answer

  5. Type II rate 0.3. What is the power?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Does a larger sample raise power? 1 yes, 0 no.

    Answer

  2. Does lowering alpha raise power? 1 yes, 0 no.

    Answer

  3. Does a larger true effect raise power? 1 yes, 0 no.

    Answer

Stretch Yourself

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

4 problems

  1. Which changes increase power?

    • A larger sample size
    • A larger true effect
    • A larger significance level
    • More variability in the population
    • Tick every box that applies.

  2. Power 0.85. What is the Type II error rate?

    Answer

  3. The False Alarm

    Rejecting a true null hypothesis. Which error? 1 Type I, 2 Type II.

    Answer

  4. The Power

    The Type II error rate is 0.2. What is the power?

    Answer