Answered: Test the claim that the standard…

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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Test the claim that the standard deviation of the ages of Phychologist in California us 7.3 at 0.01 level of significance. a random sample of 15 psychologist had a standard deviation of 6.9. Find the test value

Expert Solution

Step 1

Provided information is ;

sample size(n)=15

level of significance( $α$ )=0.01

sample standard deviation(s)=6.9

population standard deviation( $σ_{0}$ )=7.3

Null hypothesis : H₀ : $σ_{0} = 7.3$

Alternative hypothesis : H₀ : $σ_{0} \neq 7.3$

here from given information we can use chi- square test statistic to find test value ;

$χ^{2} t e s t s t a t i s t i c = \frac{n - 1}{σ^{2}} \times s^{2}$

with (n-1) degree of freedom.

Rejection criteria :

if $χ^{2}$ statistic > $χ^{2}$ critical then we reject null hypothesis

otherwise , we fail to reject the null hypothesis

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