A researcher is evaluating the influence of a treatment using a sample selected from a normally distributed population with a mean of u = 112 and a standard deviation of o = 33. The researcher expects a 22-point treatment effect and plans to use a one-tailed hypothesis test with alpha = .05. For all parts below, explain logic, show all formulas, include all steps and plug in the numbers (show all work).
a. Compute the power of the test if the researcher uses a sample of n = 33 individuals.
b. Compute the power of the test if the researcher uses a sample of n = 68 individuals.