A tool manufacturer tests three types of cutters used in lathe operations. One t

Question

A tool manufacturer tests three types of cutters used in lathe operations. 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 steel cutter developed using power 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 of ANOVA are summarized below.

SUMMARY Standard Deviation Groups Count Sum Average Variance 32 27 771.66 38 1285.54 29.84 28.58 33.83 50.13 65.12 48.02 954.88 aminated steel high-speed steel crvogenically treated steel 7.08 8.07 6.93 ANOVA Source of Variation df MS P-yalue F crit 505.26 5024.30 0.0111 3.09 Between Groups Within Groups Total 5529.56 Multiple Comparisons Pair laminated vs. high-speed laminated vs. cryogenical high-speed vs. cryogenical 0.66 2.27 2.85

Explanation / Answer

Step 1:p-value is greater than 0.01 hence we can say that option A is true

Step 2:Variation due to different cutters =505.26

Step3: F=MSbetween/MSwithin={505.26/(3-1)}/{5024.30/94}=4.734

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