Consider a random sample of size one (n = 1) from the distribution with probability function [@y(0-1), if 0 0 otherwise. f(y; 0) = 0, (a) To test Ho: 0 = 0, versus H₂ : 0 = 0₁ > 80, find a most powerful test. Let the positive constant to define the rejection region of the test be k. (b) Find the value of k so that at 0 = 2 the size of the test is 5%. (e) Obtain the power function of the test in part (a).

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
Consider a random sample of size one (n 1) from the distribution with probability
function
f(y; 0) =
[0y(0-1), if 0 <y<1 for € > 0
[o,
otherwise.
(a) To test Ho: 0 = 0, versus H₁ : 0 = 0 > 00, find a most powerful test. Let the
positive constant to define the rejection region of the test be k.
(b) Find the value of k so that at 0 = 2 the size of the test is 5%.
(c) Obtain the power function of the test in part (a).
Transcribed Image Text:Consider a random sample of size one (n 1) from the distribution with probability function f(y; 0) = [0y(0-1), if 0 <y<1 for € > 0 [o, otherwise. (a) To test Ho: 0 = 0, versus H₁ : 0 = 0 > 00, find a most powerful test. Let the positive constant to define the rejection region of the test be k. (b) Find the value of k so that at 0 = 2 the size of the test is 5%. (c) Obtain the power function of the test in part (a).
Expert Solution
steps

Step by step

Solved in 5 steps with 57 images

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman