The Relationship Between Power Values and True Mean μ in Two-Tailed Tests

A family of power curves for a two-tailed test with μ0 = 12000 will have power values closer to ____________ when μ is close to 12000 and closer to ____________ the further away μ is from 12000.

A) 0.5, 0.5
B) 1, 0
C) 0, 1
D) 0, 0

Final answer:

The correct answer is C) 0, 1, where the family of power curves for a two-tailed test with μ0 = 12000 will have power values closer to 0.5 when μ is close to 12000 and closer to 1 as μ moves farther from 12000.

Explanation:

The family of power curves for a two-tailed test with μ0 = 12000 will have power values closer to 0.5 when μ is close to 12000 and closer to 1 the further away μ is from 12000. Thus, the correct answer is C) 0, 1. The power of a test is the probability that it correctly rejects a false null hypothesis.

When the true population mean μ is very close to the hypothesized mean μ0, it is more difficult to detect a difference, and the power of the test is lower, hence approaching 0.5. However, as the true mean μ becomes further away from the hypothesized mean μ0, it is easier for the test to detect the difference, thus the power of the test increases, approaching 1. The power curve graphically represents this relationship, showing the test's power for different values of the true mean μ.