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 α = .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 0.5042 0.5014 0.4995
0.4988 0.4992
Old drill: 0.5052 0.5053 0.4947 0.4907 0.5031
0.4923 0.5040 0.5035 0.5061 0.4956
0.5035 0.4962