Please only solve question 1.13. Question 1.12 is only there for reference. Thank you. 1.12 To...

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)