Problem 1 Six different machines are being considered for use in manufacturing r

Question

Problem 1 Six different machines are being considered for use in manufacturing rubber seals. The machines are being compared with respect to tensile strength of the product. A random sample of four seals from each machine is used to determine whether the mean tensile strength varies from machine to machine. The following are the tensile-strength measurements in kilograms per square centimeter x10-1 17.5 16.4 20.3 14.6 17.5 18.3 16.9 19.2 15.7 16.719.2 16.2 15.8 17.7 17.8 20.8 16.5 17.5 18.6 15.4 18.9 18.9 20.5 20.1 Perform the analysis of variance at the 0.05 level of significance and indicate whether or not the mean tensile strengths differ significantly for the six machines. (Note that normality with common variance is assumed.) 1 Write down the null and alternative hypotheses explicitly with 's, where ' denotes the mean tensile strength of the product produced frorn machine i, i = 1,2, .6 2. Complete the following ANOVA table by filling out the 9 bold spots (2 already filled). Mean Squares MISA-SSR/(k-1) Sum o Source of Variation Su ANOVA SSA=5.34 Error SSE k(n-1) MSE-SSE/(k(n-1)) Total gree c Freedom Statistic F:- SST=67.98 kn-1 3. Calculate the p value of the F test statistic and make your conclusion in this context

Explanation / Answer

1)

ho: u1= u2 = u3=u4=u5 = u6 there is significant difference in the mean tensile strength between six machines

h1: u1 =/= u2=/= u3 =/= u4 =/= u5 =/= u6 at least one of the mean tensile strength differs significantly for six machines

2)

c)

p-value= .95355

with F =0.306 and p-value > 0.05, i fail to reject ho and conclude that

at least one of the mean tensile strength differs significantly for six machines

that is at least one of the u1 =/= u2=/= u3 =/= u4 =/= u5 =/= u6

S.V. SS df MSS F anova 5.34 =6-1 =5.34/5 =1.068/3.48 error =67.98-5.34 =23-5 =62.64/18 total 67.98 =24-1 =67.98/23

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