PracticeExamNumber3

# PracticeExamNumber3 - A tool manufacturer tests three types...

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A tool manufacturer tests three types of cutters used in a lathe operations. One type is a laminated steel cutter consisting of a 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. n is the number of cutters used of the type indicated. Average time Type of cutter until sharpening needed Standard deviation n laminated steel 29.84 7.08 32 high-speed steel 28.58 8.07 27 cryogenically treated steel 33.83 6.93 38 Assume the data are three independent SRSs, one from each of the three populations of cutters, and that the distribution of the times until sharpening is needed is normal. A partial ANOVA table is given below. Source df Sums of squares Mean square F -ratio Cutter type 505.26 Error 53.45 Total 1. The degrees of freedom for cutter type (group) are A) 2. B) 3. C) 94. D) 97. 2. The degrees of freedom for error are A) 2. B) 3. C) 94. D) 97. Page 1

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3. For this example, we notice A) this is a randomized, designed experiment. B) the data show no strong evidence of a violation of the assumption that the three populations have the same standard deviation. C) ANOVA cannot be used on these data because the sample sizes are different. D) the data show very strong evidence of a violation of the assumption that the three populations have the same standard deviation. 4. The null hypothesis for the ANOVA F test is that the population mean time until sharpening is needed is the same for all three cutter types. The alternative hypothesis is A) that the population mean time until sharpening is needed is larger for cryogenically treated steel cutters than for the other two types of cutters. B) that the population mean time until sharpening is needed is larger for high-speed steel
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## This note was uploaded on 09/25/2009 for the course IDS 371 taught by Professor Staff during the Spring '08 term at Ill. Chicago.

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PracticeExamNumber3 - A tool manufacturer tests three types...

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