Question

In: Statistics and Probability

A cookie manufacturer is concerned about whether there is an unacceptably high degree of variability in...

A cookie manufacturer is concerned about whether there is an unacceptably high degree of variability in the amount of chocolate chips that are in its most popular chocolate chip cookie. A sample of 15 cookies from the production line was collected so that a 99% confidence interval for the variance could be constructed. The sample variance was 16. Take all calculations toward the answer to three (3) decimal places, and report your answer to two (2) decimal places, without units.

The company can be 99% confident that the variance in the number of chocolate chips in the company's most popular cookie is between Blank 1 and Blank 2 .

Expert Solution

Solution :

Given that,

c = 99% = 0.99

n = 15

s² = 16

d.f. = n - 1 = 15 - 1 = 14

At 99% confidence level the is ,

= 1 - c = 1 - 0.99 = 0.01

/ 2 = 0.005 and 1 - ( / 2) = 0.995

Now , using chi square table ,

_/2,df = _0.005,14 = 31.319

_1-_/2,df = _{0.995 , 14} = 4.075

The 99% confidence interval for Variance ² is,

( 15 - 1) *16/ 31.319 < ² < ( 15 -1 ) * 16/ 4.075

7.15 < ² < 54.97

Answer :

The company can be 99% confident that the variance in the number of chocolate chips in the company's most popular cookie is between 7.15 and 54.97

orchestra answered 1 year ago

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