Let?1, ?2,… , ?? be a random sample from the normal distribution withunknownmean,? and known variance, ?2. Using a sufficient statistic for?, find the UMP test in the class of unbiased tests for testing,?0: ?= ?0 against ?1: ? ≠ ?0 at significance level ?. Let X1, X2, ..., Xn be a random sample from the normal distribution withunknown mean, µ and known variance, o². Using a sufficient statisticfor u, find the UMP test in the class of unbiased tests for testingHo: µ = µo against H1:µ # µo at significance level a.

Answered: e à random sample 1 and known varian MP…

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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Let?₁, ?₂,… , ?_? be a random sample from the normal distribution with

unknownmean,? and known variance, ?₂. Using a sufficient statistic for

?, find the UMP test in the class of unbiased tests for testing,?0: ?= ?₀ against ?₁: ? ≠ ?₀ at significance level ?.

Let X1, X2, ..., Xn be a random sample from the normal distribution with
unknown mean, µ and known variance, o². Using a sufficient statistic
for u, find the UMP test in the class of unbiased tests for testing
Ho: µ = µo against H1:µ # µo at significance level a.

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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