Question

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 x 10- Machine 6 17.5 16.4 20.3 14.6 17.5 18.3 16.9 19.2 15.7 16.7 19.2 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.

please answer using R software and include the statement of the R command to do the test of hypothesis and the R output.

thank you!

Answer 1

Null and alternative hypotheses are

Ho : Mean tensile strength does not vary with machines

Ha : Mean tensile strength varies with machines

R-code

#Read Data

X<- structure(list(m1 = c(17.5,16.9,15.8,18.6,16.4,19.2,17.7,15.4,20.3,15.7,17.8,18.9,14.6,16.7,20.8,18.9,17.5,19.2,16.5,20.5,18.3,16.2,17.5,20.1), names = c("machine1","machine1","machine1","machine1", "machine2", "machine2", "machine2", "machine2", "machine3", "machine3", "machine3", "machine3","machine4","machine4","machine4","machine4","machine5","machine5","machine5","machine5","machine6","machine6","machine6","machine6"), names=1:24), .Names = c("strength","machine"), class = "data.frame", row.names = c(NA, -23L))

dat <- X

#head(dat)
res.aov <- aov(strength ~ machine, data = dat)

anova(lm(strength ~ machine, data =dat))

Output

Analysis of Variance Table

Response: strength
          Df Sum Sq Mean Sq F value Pr(>F)
machine    5  5.338  1.0677  0.3068 0.9024
Residuals 18 62.640  3.4800               

Given, level of significance = 0.05

Since, p-value = 0.9024

0.9024 > 0.05

that is p-value > level of significance

we do not reject Ho.

Conclusion :

Mean tensile strength does not differ for the six machines