2. In the context of Example 10.2-4, where three types of fabric are tested for their flammability, materials 1 and 3 have been in use for some time and are known to possess similar flammability properties. Material 2 has been recently proposed as an alternative. Of primary interest in the study is the comparison of the joint population of materials 1 and 3 with that of material 2. Import the data into the R data frame fl and complete the following parts.

(a) Specify the contrast θ of interest, and use hand calculations to test H0 : θ = 0 vs Ha : θ ̸=0 at level of significance α = 0.05 using the procedure described in Section 10.2.1. (Hint. You may use attach(fl); sm=by(BurnL, Material, mean);

sv=by(BurnL, Material, var) to obtain the sample means and sample variances.)

(b) Combine the burn-length measurements from materials 1 and 3 into one data set, and use the rank-sum procedure for testing that the combined populations of materials 1 and 3 is the same as that of material 2. (Hint. Use the R commands x=c(BurnL[(Material==1)], BurnL[(Material==3)]);
y=BurnL[(Material==2)] ; wilcox.test(x, y).)