In hypothesis testing, if the power of a hypothesis test is 96%, which of the following statements is true about this test? a. The probability of a Type II error is 0.96. b. The probability of a Type II error is 0.04. c. The probability of a Type I error is 0.04. d. The probability of Type I error is 0.96.
Question
In hypothesis testing, if the power of a hypothesis test is 96%, which of the following statements is true about this test?
a. The probability of a Type II error is 0.96.
b. The probability of a Type II error is 0.04.
c. The probability of a Type I error is 0.04.
d. The probability of Type I error is 0.96.
Solution
The correct statement is:
b. The probability of a Type II error is 0.04.
Explanation: The power of a test is the probability that it correctly rejects the null hypothesis when the alternative hypothesis is true. It is equal to 1 minus the probability of a Type II error. So if the power of the test is 96% (or 0.96), then the probability of a Type II error is 1 - 0.96 = 0.04.
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