Measurement error in a particular situation is normally distributed with mean value l and standard deviation 4. Consider testing H₀: μ = 0 versus H_a: μ ≠ 0 based on a sample of n = 16 measurements.

a.

b.

c. What is the power of the test proposed in (b) when μ = .1 and when μ = −.1?

d. Calculate the power of the usual test when μ = .1 and when μ = −.1. Is the usual test a most powerful test?

Transcribed Image Text:

Verify that the usual test with signifi- cance level .05 rejects Ho if either x 1.96 or x≤-1.96. That this test is unbiased follows from the fact that the way to capture the largest area under the z curve above an interval having width 3.92 is to center that interval at 0 (so it extends from -1.96 to 1.96).