AP Statistics 3.8.B Type I and Type II Error Probabilities

Practise calculating Type I and Type II error probabilities from significance levels, independent repeated tests, power values, and simulated p-value distributions.

Exam points

Use alpha for one-test Type I error and complements for at least one error across independent tests.
Calculate Type II error probability as one minus power for a specified alternative.
Estimate power from simulated p-values below alpha, then use it to judge a decision rule.

[Maximum number: 1]

Suppose you did 10 independent tests of the form $H_{0}: \mu=25$ versus $H_{\mathrm{a}}: \mu<25$ , each at the $\alpha=0.05$ significance level. What is the probability of committing a Type I error and incorrectly rejecting a true $H_{0}$ with at least one of the 10 tests?

0.05

0.40

0.60

0.95

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3.8.B—Calculate the probability of Type I and Type II errors question 1