A rock climber wishes to test the tensile strength of three different types of braided ropes. She knows that the rope thickness can make a difference, so she decides to block by thickness. The tensile strengths for each rope type are given next.

(a) Test H₀: µ₁ = µ₂ = µ₃ against H₁: at least one of the means is different, where µ₁ is the mean for the nylon braided rope, µ₂ is the mean for the polyester braided rope, and µ₃ is the mean for the polypropylene braided rope, at the a = 0.05 level of significance.

(b) If the null hypothesis from part (a) was rejected, use Tukey’s test to determine which pairwise means differ using a familywise error rate of a = 0.05.

(c) Draw boxplots of the data for each treatment using the same scale to support the analytical results obtained in parts (a) and (b).

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Nylon Braided Polyester Braided Polypropylene Braided inch 2,500 1,550 1,325 3,420 inch 4,900 2,575 5,940 inch 8,400 4,170 inch 12,300 9,500 6,315