Answered: A company gives the variance in their…

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 company gives the variance in their production of a particular part as 0.051cm. Use the sample below to calculate the test statistic that would be used to determine if it has changed. Round 2 decimals. Sample size=32 Sample variance=0.08

Expert Solution

Step 1

Given:

${σ_{0}}^{2} = 0.051 c m n = 32 s^{2} = 0.08$

the significance level is taken as 0.05.

Step 2

Hypothesis:

$H 0 : σ^{2} = 0.051 H 1 : σ^{2} \neq 0.051$

Test statistic

$\begin{array}{rcl} X^{2} & = & \frac{(n - 1) s^{2}}{σ^{2}} \\ = & \frac{(32 - 1) 0.08}{0.051} \\ = & 48.627 \end{array}$

Test statistic =48.627

using the excel formula "(=CHISQ.INV((0.05/2),31)), (=CHISQ.INV.RT(0.05/2,31))" critical values are (17.539,48.232)

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