A tool manufacturer tests three types of cutters used in a lathe operation. One type is a laminated steel cutter consisting of very hard high carbon steel sandwiched between two softer steels. Another is a special high speed tool steel cutter developed using powder metallurgy. The final one is made from cryogenically treated steel. Several cutters of each type are tested to see how long they will last (in hours) in continuous operation until they need to be sharpened. The times are recorded for each cutter used in the study and the results are summarized below. Assume the data are three independent simple random samples, one from each of the three populations of cutters, and the distribution of the times until sharpening is needed is normal. Is there sufficient evidence that there is a difference in the mean time until sharpening between the three cutters at the α=.05 significance level? Laminated SteelHigh-speed SteelCryogenically Treated Steel
24.9940.3645.67
27.4626.4740.78
30.6839.9528.11
33.6726.2847.88
28.2648.5438.77
40.5532.4028.77
28.1726.1136.85
31.4744.1441.80
45.1131.3550.16
45.8236.1136.18
30.9736.7730.51
21.9032.6738.76
43.0028.2837.59
49.4448.1732.95
36.6929.3732.97
37.6434.3442.17
38.0037.7629.98
29.3616.0651.76
39.0020.4120.49
45.8646.3143.57
42.6124.3437.96
42.2321.9744.20
39.6040.9845.12
37.8623.6742.25
28.7435.3638.15
35.8128.0038.45
37.0226.2741.05
41.57 40.23
30.94 39.07
37.70 26.73
33.00 41.01
18.25 35.69
36.06
31.02
40.01
22.62
36.13
16.89
34.71