You are trying to reduce the variance in a key characteristi

You are trying to reduce the variance in a key characteristic of one of your products. The data given provides this characteristic for the current process (Column A) and a proposed improvement (Column B). Prove if the proposed improvement reduces the variance in this key characteristic (95% confidence level).

A                                                                                        B

Solution

Var(A) = 2.4675

Var(B)= 1.4065

n1=n2 = 47

Use F test to compare the variances

F = s1^2/s2^2 = 1.754

df = n1-1, n2-1 = 46,46

Set up hypotheses as:

H0: Var A = Var B

Ha: Var A>Var B

Right tailed test

p = 0.0299

At 5% sign level alpha = 0.05

As p <alpha, reject null hypothesis

Variance B is less than variance A is statistically evident at 5% sign level,.