Answered: d) Now assume that the population…

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

d) Now assume that the population standard deviation is not known. Determine that the
sample will produce a standard deviation that is as most ¾ of the population standard
deviation.
e) What assumption do you need to make for your results to be valid and determine if that
assumption is met. Explain why or why not.

Expert Solution

Step 1: Chi square distribution

(d). Let a random variable X has normal distribution with mean $mu space a n d space s tan s a r d space d e v i a t i o n space sigma$ . That is

X has N( $mu comma sigma squared$ ) distribution, where $mu space a n d space sigma space a r e space u n k n o w n$ ,then

U= $fraction numerator left parenthesis n minus 1 right parenthesis S squared over denominator sigma squared end fraction$ has a Chi square distribution with (n-1) degrees of freedom (df). Here n=36

We have to find P(S $less or equal than 3 over 4 sigma$ ). which is equivalent to

P( $S squared less or equal than 9 over 16 sigma squared$ ) = P(U $less or equal than fraction numerator 9 asterisk times 35 over denominator 16 end fraction$ ) = P(U $less or equal than$ 19.6875) = 0.01728