Quiz — Type I, Type II, Power & Choosing \( \mu_1 \) 15 T/F

1) Type I error is \( P(\text{reject }H_0 \mid H_0 \text{ true}) \) and equals \( \alpha \).

2) Type II error is \( P(\text{fail to reject }H_0 \mid H_1 \text{ true}) \) and equals \( \beta \).

3) Power is \( 1-\alpha \).

4) Holding \( n,\sigma,\mu_1 \) fixed, increasing \( \alpha \) generally decreases power.

5) In a two-sided test, \( \beta \) depends on the size of \( |\mu_1-\mu_0| \), not the sign; the same distance above or below \( \mu_0 \) gives the same \( \beta \).

6) Picking \( \mu_1 \) after seeing the data to report a larger power is valid planning practice.

7) When planning, choose \( \mu_1 \) to reflect a practically meaningful difference \( |\mu_1-\mu_0| \).

8) With the same \( \alpha \) and direction, a one-sided test usually has higher power than a two-sided test.

9) Increasing sample size \( n \) increases \( \beta \).

10) With known \( \sigma \), power calculations use \( se=\sigma/\sqrt{n} \).

11) When the true mean is \( \mu_1 \), the probability of a correct decision equals \( 1-\alpha \).

12) For fixed \( \alpha, n, |\mu_1-\mu_0| \), power does not depend on \( \sigma \).

13) For fixed \( \alpha \) and \( \mu_1 \), power is the same for one-sided and two-sided tests.

14) The p-value equals \( \beta \) when the true mean is \( \mu_1 \).

15) To make \( \beta \) smaller (more power), you should make the target difference \( |\mu_1-\mu_0| \) smaller.