6.121 Power of the mean SATM score test. Example 6.16 (page 374) gives a test of a hypothesis about the SATM scores of California high school students based on an SRS of 500 students. The hypotheses are

H₀: μ = 485
H_a: μ > 485

Assume that the population standard deviation is σ = 100. The test rejects H₀ at the 1% level of significance when z ≥ 2.326, where

Is this test sufficiently sensitive to usually detect an increase of 14 points in the population mean SATM score? Answer this question by calculating the power of the test to detect the alternative μ = 499.