Variance Comparison:

I am having a lot of trouble with the problem below. I know that the variance is smaller (I think) with the new press installed. Using megastat, the difference is .0043000 between the old and new drill, if I am doing so correctly.

A manufacturing process drills holes in sheet metal that are supposed to be .5000 cm in diameter. Before and after a new drill press is installed, the hole diameter is carefully measured (in cm) for 12 randomly chosen parts. At ? = .05, do these independent random samples prove that the new process has smaller variance? Show the hypotheses, decision rule, and test statistic.

New drill: 0.5005 0.5010 0.5024 0.4988 0.4997
0.4995 0.4976 0.5402 0.5104 0.4995
0.4898 0.4992

Old drill: 0.5052 0.5053 0.4947 0.4907 0.5031
0.4923 0.5400 0.5035 0.5601 0.4956
0.5035 0.4962

Writing or thinking "I think" is a very bad sign. Please proceed top do the assignment.

State your hypotheses: I might suggest H0: There is no difference between the variance of the two drills. Or maybe \(\displaystyle \sigma^{2}_{1} = \sigma^{2}_{2}\).

Okay, you do the next part. What is your Decision Rule?