Question

Suppose we are testing H0​:μ=−3.8 vs. H1​:μ>−3.8. We designed a test with level 10%. The test was able to achieve a power of 82% when μ=−3.1.

Complete each of the following sentences with appropriate values.
When true value of μ=−3.1, there was __probability of making a wrong decision.

Answer 1

When the true value of μ = -3.1, there is a probability of making a Type I error, which is equal to the significance level (in this case, 10%).

Step-by-step explanation:

When the true value of μ = -3.1, there is a probability of making a wrong decision known as the Type I error. In this case, the Type I error refers to rejecting the null hypothesis (H0: μ = -3.8) when it is actually true.

The probability of making a Type I error is equal to the significance level (denoted as α). Since the test was designed with a level of 10%, the probability of making a Type I error is 10% or 0.10.