Refer to the previous exercise, with y = 0 in n = 25 trials for testing H0: π = 0.50.

a. Show that 0, the maximized likelihood under H0, equals (1 − π0)25 = (0.50)25.

Show that 1, the maximized likelihood over all possible π values, equals 1.0.

(Hint: This is the value at the ML estimate value of 0.0.)

b. Show that the likelihood-ratio test statistic, 2 log(1/0), equals 34.7. Report the P-value.

c. The 95% likelihood-ratio-test-based confidence interval for π is (0.000, 0.074).

Verify that 0.074 is the correct upper bound by showing that the likelihood-ratio test of H0: π = 0.074 against Ha: π = 0.074 has a chi-squared test statistic equal to 3.84 and P-value = 0.05.