For a flip of a coin, let π denote the probability of a head. An experiment tests H 0 : π =0.5 against H a : π ≠0.5, using n s5 independent flips. a. Show that the true null probability of rejecting H...

For a flip of a coin, let π denote the probability of a head. An experiment testsH
₀: π =0.5 againstH_a
: π ≠0.5, usingns5 independent flips.

a.Show that the true null probability of rejectingH
₀ at the 0.05 significance level is 0.0 for the exact binomial test and 1 using the 1/16 large-sample score test.

b.Suppose that truly π =0.5. Explain why the probability that the 95% Clopper-Pearson confidence interval contains π equals 1.0.