8.39 Tossing a coin 10,000 times! The South African mathematician John Kerrich, while a prisoner of war during World War II, tossed a coin 10,000 times and obtained 5067 heads.
(a) Is this significant evidence at the 5% level that the probability that Kerrich’s coin comes up heads is not 0.5? Use a sketch of the standard Normal distribution to illustrate the P-value.
(b) Use a 95% confidence interval to find the range of probabilities of heads that would not be rejected at the 5% level.