On a memory task in which words are learned in a random order, it is known that people can recall a mean of 11 words with a standard deviation of 4 and that the distribution follows a normal curve. A cognitive psychologist, to test a theory, modifies that task so that the words are presented in a way in which words that have a related meaning are presented together.
The cognitive psychologist predicts that, under these conditions, people will recall so many more words that there will be a large effect size. She plans to test this with a sample of 20 people, using the .01 significance level, two-tailed.
(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 involving means of samples but has never learned about effect size or power.