Because they enable efficient procedures for evaluating answers, multiple-choice questions are commonly used on standardized tests, such as the SAT or ACT. Such questions typically have five choices, one of which is correct. Assume that you must make random guesses for two such questions. Assume that both questions have correct answers of “a.”
a. After listing the 25 different possible samples, find the proportion of correct answers in each sample, then construct a table that describes the sampling distribution of the sample proportions of correct responses.
b. Find the mean of the sampling distribution of the sample proportion.
c. Is the mean of the sampling distribution (from part (b)) equal to the population proportion of correct responses? Does the mean of the sampling distribution of proportions always equal the population proportion?