Question

1. Three different metal alloys were tested for tensile strength. The strength of some examples of each alloy measured (in hundreds of megapascals), as follows. was Alloy Tensile strength of some examples 19.8 12.4 1 15.2 14.8 2 8.9 11.6 10.0 11.9 3 10.5 13.8 12.1 Source: the data come from Berenson and Levine (1998), Business Statistics: A First Course, p. 449, Question 10.27, but shortened.) Taking the types of alloy one-way ANOVA. The following R commands were used: as groups, the lm) command in R was used to fit a strength<-c (12.4, 19.8, 15.2,14.8,8.9, 11.6, 10, 10.5, 13.8, 12.1,11.9) > alloy < test.data <data.frame (alloy,strength) > test.data$alloy strength.model <- >summary (strength . model ) > c(rep(1,4),rep(2, 3) , rep (3,4) ) <as.factor(test . data$alloy) 1m(strength al loy , test . data, model =T , x=T) (a) What is the meaning of rep (1 , 4) in the above R code? use the R command as.factor? (b) Why do we (c) Denote the two dummy variables that R has generated by I1 and 2. What names does R give to these two each example of metal alloy in the sample? (d) Create a table whose first column contains the tensile strengths, the second column contains the alloy number (group number), the third column contains the value of x, and the last column contains the value of r2 dummy variables and how are they defined for (e) Write down the theoretical regression equation for this ANOVA. Next, write down the estimated regression equation for this ANOVA. (f) Interpret the three theoretical coefficients in the above theoretical regression equation. In addition, interpret the three estimated regression coefficients in the estimated regression equation. (g) What is the overall average tensile strength of the alloys under test? (h) Perform an F-test to test whether there are differences in the population tensile strengths of the three metal alloy groups. First write down Ho and HA and then give the values of the F-statistic, the degrees of freedom, the critical values for a = 0.05 and a 0.01, and the conclusions. mean

Answer 1

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