Answered: A small diner gets eggs from 2…

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 small diner gets eggs from 2 suppliers. a sample of 50 eggs from supplier A had a STDEV of 1.1 grams. a sample from supplier B of 40 eggs had a STDEV of .75 grams.

a) Construct a 99% confidence for STDEV of supplier B

B) at a 4% confidence, conduct a hypothesis test to determine if theres any difference in STDEV between supplier a and b

Expert Solution

Step 1

The degrees of freedom is,

$\begin{array}{rcl} d f & = & 40 - 1 \\ = & 39 \end{array}$

Critical value for $χ_{U}^{2}$ :

The right-tail area is,

$\begin{array}{rcl} \frac{1 - c}{2} & = & \frac{1 - 0.99}{2} \\ = & \frac{0.01}{2} \\ = & 0.005 \end{array}$

The critical value of $χ_{U}^{2}$ at 39 degrees of freedom can be obtained using the excel formula “=CHISQ.INV.RT(0.005,39)”.

The critical value is 65.4756.

Critical value for $χ_{L}^{2}$ :

The right-tail area is,

$\begin{array}{rcl} \frac{1 + c}{2} & = & \frac{1 + 0.99}{2} \\ = & \frac{1.99}{2} \\ = & 0.995 \end{array}$

The critical value of $χ_{L}^{2}$ at 39 degrees of freedom can be obtained using the excel formula “=CHISQ.INV.RT(0.995,39)”.

The critical value is 19.9959.

The 99% confidence for STDEV of supplier B is,

$\begin{array}{rcl} \sqrt{\frac{(n - 1) s^{2}}{χ_{U}^{2}}} & < & σ < \sqrt{\frac{(n - 1) s^{2}}{χ_{L}^{2}}} \\ \sqrt{\frac{(40 - 1) 0 . 75^{2}}{65.4756}} & < & σ < \sqrt{\frac{(40 - 1) 0 . 75^{2}}{19.9959}} \\ \sqrt{0.3350} & < & σ < \sqrt{1.0971} \\ 0.5788 & < & σ < 1.0474 \end{array}$

Thus, the 99% confidence for STDEV of supplier B is $\begin{array}{rcl} 0.5788 & < & σ < 1.0474 \end{array}$ .

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