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Cogito

Integrated Math 3 · Chapter 7 · Lesson 3

Practice Worksheet

Significance Tests

Could chance alone explain this?

12 problems · about 22 minutes · S-IC.B.5, S-IC.B.6

NameDate

Figure — use these to answer the problems

Widen the gap between observed and expected. The larger it grows, the harder chance alone is to believe.
Observed62
Expected50
Observed62
Expected under the null50
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. p-value 0.30 at the 0.05 level. Significant? 1 yes, 0 no.

    Answer

  2. What exactly does a p-value measure?

    • The chance of data this extreme, assuming the null is true.
    • The probability that the null hypothesis is true.

  3. p-value 0.01 at the 0.05 level. Significant? 1 yes, 0 no.

    Answer

  4. p-value 0.20 at the 0.05 level. Significant? 1 yes, 0 no.

    Answer

  5. Which hypothesis states no effect? 1 null, 2 alternative.

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. A fair coin, 100 tosses. Expected heads?

    Answer

  2. The usual significance threshold, as a decimal?

    Answer

  3. Does a smaller p-value mean more surprising under the null? 1 yes, 0 no.

    Answer

Stretch Yourself

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

4 problems

  1. Put a significance test in order.

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

    • State the null and alternative hypotheses.
    • Collect data and compute the statistic.
    • Find the p-value, assuming the null is true.
    • Compare to the threshold and conclude in context.

  2. p-value 0.049 at the 0.05 level. Significant? 1 yes, 0 no.

    Answer

  3. The Decision

    p-value 0.02 at the 0.05 level. Is the result significant? 1 yes, 0 no.

    Answer

  4. The Non-Result

    p-value 0.40. Does this prove the null is true? 1 yes, 0 no.

    Answer