Chapter 8, Problem 20P

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 $\mu =240$ and $\sigma =30$ .

a. If the researcher uses a two-tailed test with $\alpha =.05$ , what is the power of the hypothesis test?

b. Again assuming a two-tailed test with $\alpha =.05$, what is the power of the hypothesis test if the sample size is increased to $n=25$?