Let X₁,..., Xn Uniform [0, 0o] be iid with unknown upper end point 00. Sup- pose you observe data ₁,..., n. Recall further that The MLE was given by: ê= max{₁} and the density of the estimator is given by (X) n-1 {* (*)** 0 foo (0(X) = z) = = if z = [0,00] otherwise Suppose that data is observed. You are told that the observed value of the MLE is 34.76 and that the sample size was 40. (a) It is conjectured by a student that the true value of 0o is 35. Their lecturer says that actually they think it is bigger than that. Using the MLE as the test statistic, setup a hypothesis test for this scenario and calculate the p-value. (b) Under this setting how large would the observed value of the MLE have to be to get the p-value smaller than 0.05? (c) It is conjectured by a different student that the true value of 00 is 25. Their lecturer says that they are confident that it is bigger than that. Using the MLE as the test statistic, setup a hypothesis test for this scenario and calculate the p-value in this case. (d) It is conjectured by a student that the true value of 0o is 35. Their lecturer says that actually they think it is less than that. Using the MLE as the test statistic, setup a hypothesis test for this scenario and calculate the p-value.
Let X₁,..., Xn Uniform [0, 0o] be iid with unknown upper end point 00. Sup- pose you observe data ₁,..., n. Recall further that The MLE was given by: ê= max{₁} and the density of the estimator is given by (X) n-1 {* (*)** 0 foo (0(X) = z) = = if z = [0,00] otherwise Suppose that data is observed. You are told that the observed value of the MLE is 34.76 and that the sample size was 40. (a) It is conjectured by a student that the true value of 0o is 35. Their lecturer says that actually they think it is bigger than that. Using the MLE as the test statistic, setup a hypothesis test for this scenario and calculate the p-value. (b) Under this setting how large would the observed value of the MLE have to be to get the p-value smaller than 0.05? (c) It is conjectured by a different student that the true value of 00 is 25. Their lecturer says that they are confident that it is bigger than that. Using the MLE as the test statistic, setup a hypothesis test for this scenario and calculate the p-value in this case. (d) It is conjectured by a student that the true value of 0o is 35. Their lecturer says that actually they think it is less than that. Using the MLE as the test statistic, setup a hypothesis test for this scenario and calculate the p-value.
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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