A study of fill volumes is conducted at a food canning facto

A study of fill volumes is conducted at a food canning factory to determine the level of consistency between the two filling lines, A and B. A random sample of 11 cans taken from line A has a sample average of 8.005 ounces and a sample standard deviation of 0.013 ounces. A similar sample of 16 cans is obtained from line B with a sample average of 7.997 ounces and a sample standard deviation of 0.009 ounces. The quality control manager is interested in finding evidence at the 0.01 level that there is a difference in the variance in fill volume for the two lines. Give the value of the test statistic suggested by the testing situation described above. a. 3.45 b. 4.69 c. 6.76 d. 2.64 e. 2.09

Solution

here,

let A has variance sigma₁²

B has variance sigma₂².

now, H₀: sigma₁² = sigma₂² vs. H₁: sigma₁² not equal to sigma₂².

let s₁² and s₂² be the sample variances of A & B respectively.

And, they are unbiased estimate of the variances.

let m and n be the sample size for A & B.

so, (m-1)s₁²/sigma₁² follows chi square distn with (m-1) d.f.

similarly, (n-1)s₂²/sigma₂² follows chi square distn with (n-1) d.f.

now, under H0, F = s₁²/s₂² follows F-dist. with (m-1,n-1) d.f.

So, test statistic = F = s₁²/s₂² = (0.013/0.009)² = 2.09

So, the value of the test statistic is e)2.09