1.13 Refer to the previous exercise, with y = 0 in n = 25 trials for testing H0: π = 0.50. Show that l0, the maximized likelihood under H0, equals (1 − π0)25 = (0.50)25. Show that l1, the maximized likelihood over all possible π values, equals 1.0. (Hint: This is the value at the ML estimate value of 0.0.) Show that the likelihood-ratio test statistic, 2 log(l1/l0), equals 34.7. Report the P -value. 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.
1.13 Refer to the previous exercise, with y = 0 in n = 25 trials for testing H0: π = 0.50.
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Show that l0, the maximized likelihood under H0, equals (1 − π0)25 = (0.50)25. Show that l1, the maximized likelihood over all possible π values, equals 1.0.
(Hint: This is the value at the ML estimate value of 0.0.)
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Show that the likelihood-ratio test statistic, 2 log(l1/l0), equals 34.7. Report the P -value.
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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.
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