Answered: then the value of the test statistic…

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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Question

A sample of size 20 has a mean of 44 and a standard deviation of 3. Assuming the population is distributed N(μ,σ2) and H0: σ2 = 64 versus H1: σ2 < 64 is to be tested at level α = 0.10, then the value of the test statistic and the critical value (cut-off-value), respectively, are

Expert Solution

Step 1

Given values are-

Sample size (n)=20

Sample mean =44

Sample standard deviation=3

Population variance ( $σ^{2}$ )=64
Significance level $α = 0.10$

Sample variance will be = (sample standard deviation)²

Sample variance (s²)=9

Degree of freedom=n-1=20-1=19

Null Hypothesis given -

$H_{0} : σ^{2} = 64 H_{1} : σ^{2} < 64$

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