Question

An experiment was conducted to compare the alcohol content of soy sauce on two different production lines. Production was monitored eight times a day in both production lines. Production line 1 has a sample standard deviation of 0.16 and Production line 2 has a sample standard deviation of 0.11. Assume both populations are normal.

State and conclude your hypothesis at the 0.05 level of significance if the both of production lines have the same variability?

Answer 1

Solution:

Here, we have to use F-test for the difference between two population variances.

H0: σ12 = σ22 versus Ha: σ12 ≠ σ22

This is a two tailed test.

We are given

Level of significance = α = 0.05

The test statistic formula is given as below:

F = S1^2/S2^2

We are given

S1 = 0.16

S2 = 0.11

F = 0.16^2/0.11^2

F = 2.115702

N1 = 8

N2 = 8

DF1 = N1 – 1 = 7

DF2 = N2 – 1 = 7

P-value = 0.172014

(by using F-table)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is sufficient evidence to conclude that the both of production lines have the same variability.