Suppose that an ESP test consists of n = 75 independent tries, for which there are four possible choices on each try. Suppose that someone is just guessing, so the probability of a correct guess on each try is p = .25. Consider two possible sample proportions: P^ = .20 (15 correct) and P^ =.33 (25 correct).
a. Find the standardized z-statistics for P^ =.20 and P^ =.33.
b. Draw a picture of the sampling distribution of P^, and identify where P^ =.20 and P^ =.33 fall on the picture.
c. Draw a picture of the standard normal curve, and identify where the standardized statistics found in part (a) fall on the picture.
d. What is the relationship between the pictures in parts (b) and (c)?