We have a sample of 16 computer runs, covering a range of production
jobs, showed that the standard deviation of the processing time was 22
(hundredths of a second) for the new machine and 12 (hundredths of a
second) for the current machine. At the .05 significance level can we
conclude that there is more variation in the processing time of the
new machine?

We use an F-test to determine if the two standard deviations are equal
or if standard deviation 1 (s1) is greater than standard deviation 2
(s2).  Therefore, the null hypothesis is that the standard deviations
are equal, while the alternative hypothesis is that s1 is greater than
s2 for an upper one tailed test.

F = 22^2/12^2 = 3.3611.

alpha = 0.050

If F > F(alpha, N1-1, N2-1), then s1 is believed to be greater than
s2, thereby rejecting the null hypothesis.  I am assuming that each
machine ran 16 times, so N1=N2=16.

F(0.050, 15, 15) is 2.4 (Source:  Introduction to the Practice of
Statistics by Moore & McCabe, W. H. Freeman and Company (1989) Table
F).

Since 3.3611 > 2.4, we reject the null hypothesis that s1 = s2 and can
conclude that s1 > s2 at the 0.05 significance level.

Source:   "1.3.5.9. F-Test for Equality of Two Standard Deviations"
Engineering Statistics Handbook
http://www.itl.nist.gov/div898/handbook/eda/section3/eda359.htm

Sincerely,

Wonko

Hi.
The F-test is suited to two sets of data from "Normal" distributions.
If they are not, then the test will give you a misleading level of
confidence. It is a good idea to plot the data used to form each SD (a
"stem-and-leaf" plot is OK).

I would be concerned if a few points are outliers, particularly if
they are on one side of the mean.

I would probably try and have the same tasks for both machines, so
that you can be sure that one of them didn't get a harder set to work
on.