A researcher plans to conduct an experiment evaluating the effect of a treatment. A sample of n = 9 participants is selected and each person receives the treatment before being tested on a standardized dexterity task. The treatment is expected to lower scores on the test by an average of 30 points. For the regular population, scores on the dexterity task form a normal distribution with µ = 240 and s = 30.
a. If the researcher uses a two-tailed test with a = .05, what is the power of the hypothesis test?
b. Again assuming a two-tailed test with a = .05, what is the power of the hypothesis test if the sample size is increased to n = 25?