2. HARDER: Now assume the setting of Tutorial sheet 2. Recall: Let X₁, Xn Uniform [0, 0o] be iid with unknown upper end point 00. Sup- pose you observe data 2₁,..., Xn. Recall further that The MLE was given by: ê= max{₁} i and the density of the estimator is given by 6(X) n-1 {* (*)** 0 foo(Đ(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 0o is 25. Their lecturer says that they are confident that it is bigger than that. Using the MLE as the test statistic, set up 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 00 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.
2. HARDER: Now assume the setting of Tutorial sheet 2. Recall: Let X₁, Xn Uniform [0, 0o] be iid with unknown upper end point 00. Sup- pose you observe data 2₁,..., Xn. Recall further that The MLE was given by: ê= max{₁} i and the density of the estimator is given by 6(X) n-1 {* (*)** 0 foo(Đ(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 0o is 25. Their lecturer says that they are confident that it is bigger than that. Using the MLE as the test statistic, set up 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 00 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
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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please don't use R！
![2. HARDER: Now assume the setting of Tutorial sheet 2. Recall:
Let X₁,..., Xn Uniform [0, 00] be iid with unknown upper end point 00. Sup-
pose you observe data x₁,..., xn.
Recall further that The MLE was given by:
Ô =max{z}
and the density of the estimator is given by Ô(X)
n-1
n
- { * (*) **
00
foo(Đ(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 00 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 00 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53d0abe2-4cb5-4db5-bef8-ebd7977db539%2Fb9bcbc3b-ed92-4bf1-9f59-d465070ea7d4%2F9ht2qi6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. HARDER: Now assume the setting of Tutorial sheet 2. Recall:
Let X₁,..., Xn Uniform [0, 00] be iid with unknown upper end point 00. Sup-
pose you observe data x₁,..., xn.
Recall further that The MLE was given by:
Ô =max{z}
and the density of the estimator is given by Ô(X)
n-1
n
- { * (*) **
00
foo(Đ(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 00 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 00 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.
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