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. A random sample of each of the three types is 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 and multiple comparison are summarized below. Average SUMMARY Groups laminated steel high-speed steel cogenically treated steel Count 35 35 35 Sum 9153.05 1090 95 1144.15 Standard Variance Devinton 179 423 63 04 7.94 33.87 3117 2269 d ANOVA Source of Vacation Between Groups Within Groups MS F SS 555 67 3903.50 P-value 00011 Font 3.09 Total 4459 37 Multiple Comparisons laminated high-speed laminated cryogenical high-speed veryogenical 3.69 -103 For items 1 - 3. find the corresponding statistics. For items 4-7.determine if each statement is supported by the multiple comparisons. Use family a=5% 1. The variation is due to the different types of the cutters Choose 2. The degrees of freedom for the numerator and the denominator of the statistic Choose 3. The ANOVA Fstatistic Choose 4. Wong the three types of cutters, the cryogenically treated steel cutter has the rest Choose population mean 5. The high speed cutter lasts longer than the farminated steel cutter Choose 6. The cryogenically treated cutter lasts longer than the high-speed cutter Choose 7. Among the three types of cutters, the laminated steel cutter has the smallest population mean Choose
all of them

Answer 1

Sol:

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To answer this question lets understand what is the meaning of R^2. R^2 basically tells what percent of variance response (dependent) variable
is explained by variance of predictors (independent) variables.

Here R Square is the ratio of SS between = 416.12 and total SS = 5071.03

R Square = 416.12/5071.03

= 0.0821 or 8.21% or 8% ( rounding off to nearest integer)

Answer: 8% of variation is due to different types of the cutters