Scores on the Wechsler Intelligence Scale for Children (WISC) in neurotypical children have a population mean of 100 and a population standard deviation of 15. Assume the population standard deviation is the same in neurotypical and autistic children, but the population mean in autistic children is unknown.
a) Suppose we take a sample of 49 autistic children. What is the critical value (on the x^bar scale) for a one-sided Neyman-Pearson hypothesis test of H0 : μ = 100 vs. H 1 : μ = 95 using alpha = 0.05? Round your answer to 3 decimal places.
b)Using your critical value, what is the power of our test? Express your answer as a decimal rounded to the nearest thousandth (3 decimal places).
c)The probability of committing a Type II Error on this test is: