Question

If the alternative hypothesis is true, then the probability of making a type 2 error and the power of a test add up to 1.

a. True
b. False

Answer 1

The probability of making a Type II error and the power of a test do not add up to 1 when the alternative hypothesis is true.

Step-by-step explanation:

The statement is b. False.

The probability of making a Type II error and the power of a test do not add up to 1 when the alternative hypothesis is true. Instead, the power of a test represents the probability of correctly accepting a true alternative hypothesis, while the Type II error represents the probability of incorrectly failing to reject a false null hypothesis. Both probabilities are independent and can be adjusted by changing the sample size and significance level of the test.

For example, if a significance level of 0.05 is used and the power of the test is 0.80, it means there is a 5% chance of making a Type I error (rejecting the null hypothesis when it is true) and a 20% chance of making a Type II error (failing to reject the null hypothesis when it is false).