MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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
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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