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Cogito

AP Statistics · Chapter 8 · Lesson 1

Practice Worksheet

Simulation and Randomisation

Building a sampling distribution by hand.

12 problems · about 21 minutes · VAR-1.E, UNC-3.C

NameDate

Figure — use these to answer the problems

A simulated distribution. The observed result is judged against how often chance alone reaches it.
Low12
Middle30
High8
Low outcomes12
Middle outcomes30
High outcomes8
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. 20 of 1000 simulated results were at least as extreme. Estimated p-value?

    Answer

  2. What is assumed while building a randomisation distribution?

    • The null hypothesis, that there is no effect.
    • The alternative hypothesis.

  3. 50 of 1000 trials were as extreme. Estimated p-value?

    Answer

  4. 8 of 200 trials were as extreme. Estimated p-value?

    Answer

  5. 300 of 1000 trials were as extreme. Estimated p-value?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. That p-value at alpha 0.05. Significant? 1 yes, 0 no.

    Answer

  2. Which gives a steadier estimate? 1 for 20 trials, 2 for 2000.

    Answer

  3. What is assumed true while simulating? 1 the null, 2 the alternative.

    Answer

Stretch Yourself

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

4 problems

  1. Put the simulation design in order.

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

    • State what one trial represents.
    • Decide how the randomness maps onto the situation.
    • Define what counts as a success.
    • Run many trials and compute the proportion as extreme.

  2. 10 of 500 trials were as extreme. Estimated p-value?

    Answer

  3. The Estimate

    30 of 1000 simulated results were at least as extreme. What is the estimated p-value?

    Answer

  4. The Decision

    That p-value at alpha 0.05. Is the result significant? 1 yes, 0 no.

    Answer