Suppose you flip a coin 100 times and get 58 heads. (a) Test that heads and tails are
equally likely at α = .05 using a chi-square goodness-of-fit test. (b) Test the hypothesis
H0 : p = P(Heads) = 1/2 using the standard test for proportions in Section 10.2. (c) Do
the tests lead to the same conclusion? Are the tests equivalent, that is, can the test statistic
in one test be written as a function of the test statistics of the other in such a way that they
both always lead to the same conclusion regarding H0 at the same significance level given
the same data?