A statistics instructor would like to ask ‘‘clicker” questions that about 80% of her students in a large lecture class will get correct. A higher proportion would be too easy and a lower proportion might discourage students. Suppose that she tries a sample of questions and receives 76 correct answers and 24 incorrect answers among 100 responses. The hypotheses of interest are H₀: p = 0.80 vs H_a: p ≠ 0.80. Discuss whether or not the methods described below would be appropriate ways to generate randomization samples in this setting. Explain your reasoning in each case.

(a) Sample 100 answers (with replacement) from the original student responses. Count the number of correct responses.

(b) Sample 100 answers (with replacement) from a set consisting of 8 correct responses and 2 incorrect responses. Count the number of correct responses.