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Let Y < Y2 < Y3 < Y, be the order statistics of a random sample of size n = 4 from a distribution with pdf f(r; 0) = . 0 0. The hypothesis Ho : 0 =1 is rejected and H1 : 0 > 1 is accepted if the observed YA 2 e. Find the constant e so that the significance level is a = 0.05. & Determine the power function of the test.

Let Y < Y2 < Y3 < Y, be the order statistics of a random sample of size n = 4 from a distribution with pdf f(r; 0) = . 0 0. The hypothesis Ho : 0 =1 is rejected and H1 : 0 > 1 is accepted if the observed YA 2 e. Find the constant e so that the significance level is a = 0.05. & Determine the power function of the test.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Please see attached statistical mathematics question. How to find the constant c so that the signi cance level is alpha = 0.05.
and determine the power function of the test?

Let \( Y_1 < Y_2 < Y_3 < Y_4 \) be the order statistics of a random sample of size \( n = 4 \) from a distribution with probability density function (pdf) \( f(x; \theta) = \frac{1}{\theta}, \) for \( 0 < x < \theta, \) and zero elsewhere, where \( \theta > 0 \). The hypothesis \( H_0: \theta = 1 \) is rejected and \( H_1: \theta > 1 \) is accepted if the observed \( Y_4 \geq c \). - **Objective**: Find the constant \( c \) such that the significance level is \( \alpha = 0.05 \). - **Additionally**: Determine the power function of the test.
Transcribed Image Text:Let \( Y_1 < Y_2 < Y_3 < Y_4 \) be the order statistics of a random sample of size \( n = 4 \) from a distribution with probability density function (pdf) \( f(x; \theta) = \frac{1}{\theta}, \) for \( 0 < x < \theta, \) and zero elsewhere, where \( \theta > 0 \). The hypothesis \( H_0: \theta = 1 \) is rejected and \( H_1: \theta > 1 \) is accepted if the observed \( Y_4 \geq c \). - **Objective**: Find the constant \( c \) such that the significance level is \( \alpha = 0.05 \). - **Additionally**: Determine the power function of the test.
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