You are given a single random observation from either the Uniform distribution on (−2, 2) or the standard Normal distribution. a) Accurately sketch a picture of the null and alternative densities on one set of axes.b) Find the most powerful test of size a = 0.02 forHo X Uniform(-2, 2)versusH₁: X~ Normal(0, 1²).(Hint: Be careful when determining the rejection region of the test.)c) Calculate the power, 7, of the test.d) Calculate the probability of Type II Error, ß, for the test.

The size is given as α=0.02. The hypotheses are given as follows: H0: X~Uniform-2, 2H1: X~Normal0,12…

Answered: a) Accurately sketch a picture of the…

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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You are given a single random observation from either the Uniform distribution on (−2, 2) or the standard Normal distribution.

a) Accurately sketch a picture of the null and alternative densities on one set of axes.
b) Find the most powerful test of size a = 0.02 for
Ho X Uniform(-2, 2)
versus
H₁: X~ Normal(0, 1²).
(Hint: Be careful when determining the rejection region of the test.)
c) Calculate the power, 7, of the test.
d) Calculate the probability of Type II Error, ß, for the test.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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