23. ADVANCED TOPIC: A psychologist is planning a study on the effect of motivation on performance on an attention task. In this task, participants try to identify target letters in a stream of letters passing by at a rapid rate. The researcher knows from long experience that, under ordinary experimental conditions, the population of students who participate in this task identify a mean of 71 of the key letters, that the standard deviation is 10, and that the distribution is approximately normal. The psychologist predicts that, if the participant is paid a dollar for each letter identified correctly, the number correctly identified will increase to 74. The psychologist plans to test 20 participants under these conditions, using 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 involving means of samples but has never learned about power.