Errors and Power Practice

Question

Question 7 (1 point)

Consider a hypothesis test in which the significance level is α=0.05 and the power of the test is 0.65. What is the probability of making a Type II error?

a	0.65
b	0.05
c	0.60
d	0.95
e	0.35

Question 8 (1 point)

If all else is constant, which of the following would result in a decrease of the probability of a Type II error?

a	The true parameter is closer to the null
b	The standard error is increased
c	The sample size is increased
d	Type II cannot be decreased, only increased
e	The significance level is decreased

Question 9 (1 point)

Suppose that on a hypothesis test for a single population mean, Ha: μ < 10. Assume that Ha is true. For a fixed sample size and significance level α, the power of the test will be greatest if the actual mean is which of the following?

a	10
b	8
c	13
d	9
e	11

Question 10 (1 point)

An environmental scientist wants to test the null hypothesis that an antipollution device for cars is not effective. Under which of the following conditions would a Type I error be committed?

a	The scientist concludes that the antipollution device is effective when it actually is.
b	The scientist concludes that the antipollution device is not effective when it actually is not.
c	The scientist concludes that the antipollution device is not effective when it actually is.
d	The scientist concludes that the antipollution device is effective when it actually is not.
e	A Type I error cannot be committed in this situation.

Answer 1

Type II error probability = 1 - power, so if power is 0.65, the probability of making a Type II error is 1 - 0.65 = 0.35 (e)

The probability of a Type II error is decreased if you increase the sample size.(c)

The power of the test would be greatest if the mean was actually 8 because you would be more likely to accept the alternate hypothesis. (b)

A Type I error is committed if you reject the null hypothesis when it is true, so the answer would be (d).