Based on a particular theory of creativity, a psychologist predicts that artists will be greater risk takers than the general population. The general population is normally distributed with a mean of 50 and a standard deviation of 12 on the risk-taking questionnaire this psychologist plans to use. The psychologist expects that artists will score, on the average, 55 on this questionnaire. The psychologist plans to study 36 artists and test the hypothesis at the .05 level.
(a) What is the power of this study?
(b) Sketch the distributions involved, showing the areas for alpha, beta, and power.
(c) Explain your answer to someone who understands hypothesis testing with means of samples but has never learned about power.