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Please only solve question 1.13. Question 1.12 is only there for reference. Thank you. 1.12 To collect data in an introductory statistics course, recently I gave the students a questionnaire. One question asked whether the student was a vegetarian. Of 25 students, 0 answered yes. They were not a random sample, but let us use these data to illustrate inference for a proportion. (You may wish to refer to Section l-4-1 on methods of inference.) Let π denote the population proportion who would say yes. Consider Ho: 0.50 and Ha:0.50.

1.13 Refer to the previous exercise, with y -0 in 25 trials. a. Show that10, the maximized likelihood under Ho, equals (1-T0)25, which is (0.50)25 for Ho: π-0.50. b. Show that &1, the maximum of the likelihood function over all possible T values, equals 1.0. (Hint: This is the value at the ML estimate value of 0.0.) c. For H: π-0.50, show that the likelihood-ratio test statistic, -2 log(lo/e), 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 Upon completion of the question also please show how to obtain the 95% likelihood-ratio confidence interval for for part (d)

math   Statistics-And-Probability   
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2s n-1 lo 2S 1292 = 34F2S 2S 3 84, 5 psi

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