Question

A consumer advocacy group is concerned about the variability in the cost of prescription medication. The group surveys eight local pharmacies and obtains the following prices (in %) for a particular brand of medication: (You may find it useful to reference the appropriate table: chi-square table or F table) 25.50 22.00 30.00 30.00 24.50 22.50 38.00 36.50 Click here for the Excel Data File a. Calculate the point estimate for the population variance. (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.) Point estimate b. The group assumes that the above prices represent a random sample drawn from a normally distributed population. Construct the 90% interval estimate for the population variance. (Round your answers to 2 decimal places.) Confidence interval c. The group decides to begin a lobbying effort on its members' behalf of the variance in the price does not equal 6. What should the group do? O The group should begin on its lobbying effort. O The group should not begin on its lobbying effort.

Answer 1

a )

Sample variance ( s² ) is best point estimate of population variance ( $\sigma ^2$ )

We have to find sample variance.

Using Excel , =VAR( )

ww 24.5 22.5 36.5 10 =VAR(A1:A3) 11

Variance = s² = 37.41071

b)

We have to find 90% confidence interval for population variance.

Formula :

(n-1)s 2 xổ 2,1-1 (n − 1) s- Xí-a/2,n=1

Where ,

n is sample size = 8 , Variance = s² = 37.41071

is right tail chi-square critical value at given confidence level.

Xa/2.n-1

Confidence level = 90% = 0.9  

Significance level = $\alpha$ = 1 - 0.9 = 0.1 , $\alpha$ /2 = 0.05

So, right tail critical value is ,

Xa/2.n-1
=
ΧΟ, 05,7
= 14.0671

{ Using Excel function , =CHIINV(0.05,7 ) = 14.0671 }

is left tail critical value.

Xi-a/2.n-1

Xi-a/2.n-1
=
xổ 45 = 2.16735

{ Using Excel function , =CHIINV(0.95,7 ) = 2.1673 }
  

So, 90% confidence interval of population variance is ,

(8 - 1)37.4107 14.0671 <o (8 - 137.4107 <! 2.1673

18.62 <σ' < 120.83

Confidence interval = 18.62 to 120.83

c)

Te group decides to begin a lobbying effort on it's members' behalf if the variance in the price does not equal 6

From part b , it is observed that limits of  confidence interval is greater than 6

So, the group should begin on its lobbying effort.