Answered: A small diner gets its eggs from two…

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 its eggs from two different suppliers. Uniformity of the weight of the eggs is an important quality parameter on which the suppliers are judged. A sample of 35 eggs from supplier A had a standard deviation in weight of 1.2 gm, while a sample of 45 eggs from supplier B had a standard deviation of .85gm in weight.

USING EXCEL:

a. Construct a 99% confidence interval for the standard deviation of the weight of eggs provided by supplier A

b. At a 2% significance, conduct the appropriate hypothesis test to determine if there is any difference in the standard deviation of weight of eggs provided by the two suppliers.

Expert Solution

Step 1

Given
For supplier A
sample size $= 35$
standard deviation $= 1.2$

For supplier B
sample size $= 45$
standard deviation $= 0.85$

a)
The confidence interval for standard deviation is calculated using the below shown formula
$c o n f i d e n c e i n t e r v a l = (s {(\frac{n - 1}{χ_{1 - \frac{α}{2}, n - 1}^{2}})}^{\frac{1}{2}}, s {(\frac{n - 1}{χ_{\frac{α}{2}, n - 1}^{2}})}^{\frac{1}{2}})$
For supplier A
s $= 1.2$
n $= 35$
degree of freedom $= n - 1 = 34$
As we need 99% confidence interval
$α = 1 - 0.99 = 0.01$
$1 - \frac{α}{2} = 0.995 \frac{α}{2} = \frac{0.01}{2} = 0.005$

Using Excel function CHISQ.INV(Probability, degree of freedom) we find the critical values
Entering the following function in excel we get
=CHISQ.INV(0.995,34) = 58.96393
=CHISQ>INV(0.005,34) = 16.50127

Using these values we get the 99% confidence interval as shown below
$\begin{array}{rcl} c o n f i d e n c e i n t e r v a l & = & (s {(\frac{n - 1}{χ_{1 - \frac{α}{2}, n - 1}^{2}})}^{\frac{1}{2}}, s {(\frac{n - 1}{χ_{\frac{α}{2}, n - 1}^{2}})}^{\frac{1}{2}}) \\ l o w e r l i m i t & = & s {(\frac{n - 1}{χ_{1 - \frac{α}{2}, n - 1}^{2}})}^{\frac{1}{2}} \\ = & 1.2 {(\frac{35 - 1}{58.96393})}^{\frac{1}{2}} \\ = & 0.911 \\ u p p e r l i m i t & = & s {(\frac{n - 1}{χ_{\frac{α}{2}, n - 1}^{2}})}^{\frac{1}{2}} \\ = & 1.2 {(\frac{35 - 1}{16.50127})}^{\frac{1}{2}} \\ = & 1.723 \end{array}$
The 99% confidence interval for standard deviation of weight of eggs provided by supplier A is (0.911, 1.723)

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