Question

In the filling od drink pouches, too much variation can cause problems for the manufacturer. Regardless of the flavor or the volume of the container, the variability is to remain constant. The machine filling the Grape flavor was right for the last test with a variance of 2.30 grams based on a sample of size 16. The machine filling the fruit flavor had a variance of 2.58 grams for a sample of 16. Assuming the distribution of the fills for each machine is approximately normal, is there evidence to show that the variability for the machine filling the fruity flavor is higher than the machine filling the grape flavor?

Answer 1

We have to test, H0: = against H1: > ,

where and are the standard deviations of the machines filling fruit flavor and grape flavor respectively.

The test-statistic is given by, F =

Thus, F = 2.58/2.30 = 1.1217

Under H0, F ~ . i.e. F ~

The p-value = P(F > 1.1217) = 0.41

Assuming 5% level of significance, p-value > level of significance (0.05).

So, we fail to reject the null hypothesis H0.

We conclude there is not sufficient evidence to claim that the variance of machine filling fruit flavor is higher than machine filling grape flavor.