To demonstrate the differences between flipping and spinning, Professors A. Gelman and D. Nolan modified a checker by adding putty to the crown side, calling it heads. In 100 flips of the checker, they observed 54 heads. In 100 spins of the checker, they observed 23 heads. The results for the flips are consistent with the model that the probability of heads is 0.5, even with the putty. Are the results for the spins of checkers with putty consistent with the model that the probability of heads is 0.5? [Source: stat-www.berkeley.edu.]
a. Answer the question by using inference for a proportion, as in Chapter 8.
b. Answer the question by using a chi-square goodness-of-fit test.
c. Compare the two results in parts a and b.