Refer to the previous exercise, with y = 0 in n = 25 trials. a. Showthat 0, the maximized likelihood underH0, equals (1 0)25,

Refer to the previous exercise, with y = 0 in n = 25 trials.

a. Showthat 0, the maximized likelihood underH0, equals (1 − π0)25, which is (0.50)25 for H0: π = 0.50.

b. Show that 1, the maximum of the likelihood function over all possible π

values, equals 1.0. (Hint: This is the value at the ML estimate value of 0.0.)

c. For H0: π = 0.50, show that the likelihood-ratio test statistic,

−2 log(0/1), equals 34.7. Report the P-value.

d. The 95% likelihood-ratio 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 chi-squared test statistic equal to 3.84 and P-value = 0.05.