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In an experiment to assess the effects of curing time(factorA) and type of mix (factor

ISBN: 9781305251809 122

Solution for problem 16 Chapter 11.2

Probability and Statistics for Engineering and the Sciences | 9th Edition

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Problem 16

In an experiment to assess the effects of curing time(factorA) and type of mix (factor B) on the compressivestrength of hardened cement cubes, three different curingtimes were used in combination with four differentmixes, with three observations obtained for each of the12 curing timemix combinations. The resulting sums ofsquares were computed to be SSA 5 30,763.0, SSB 534,185.6, SSE 5 97,436.8, and SST 5 205,966.6.a. Construct an ANOVA table.b. Test at level .05 the null hypothesis H0AB: all gijs 5 0(no interaction of factors) against HaAB: at least onegij 0.c. Test at level .05 the null hypothesis H0A: a1 5 a25a3 5 0 (factor A main effects are absent) against HaA: atleast one ai 0.d. Test H0B: b1 5 b2 5 b3 5 b4 5 0 versus HaB: at leastone bj 0 using a level .05 test.e. The values of the xi??s were x1?? 5 4010.88, x2?? 54029.10, and x3?? 5 3960.02. Use Tukeys procedureto investigate significant differences among the threecuring times.

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