In: Statistics and Probability
A manufacturer is interested in the output voltage of a power supply used in a PC. Output voltage is assumed to be normally distributed, with standard deviation 0.25 V, and the manufacturer wishes to test H0: μ = 9 V against H1: μ ≠ 9 V with a sample of n = 10 units.
(a) The critical region is defined as , find the type I error probability α.
(b) Find the power of the test for detecting a true mean output voltage of 9.1 V.
c) Find the type I error probability α and the power of the test when n = 16 batches and the boundaries of the critical region do not change.
(d) Suppose that the process engineer wants the type I error probability for the test to be α = 0.05. Where should the critical region be located?