3. (20 points) A chemist wishes to test the effects of three chemical agents on the strength of a particular type of cloth. Because there might be variability from one bolt to another, the chemist found two bolts and applies all three chemicals in random order to each bolt. The resulting tensile strengths follow. Bolt Chemical 73 68 73 67 75 69 (a) Which type of design has been possibly employed here? Explain which how the fundamental principles of experimental designs are applied here. (b) How many different equally likely data sets can be generated from this data for the randomization test for no chemical effect on tensile strength? (c) Perform a hypothesis test to check whether there is any difference in average tensile strength for the three chemical agents without assuming normality of tensile strength. Clearly describe how you performed the test (with a=0.05). State clearly the hypotheses, test statistic, decision rule, and your conclusion. (d) Now write down the usual parametric model which is used to study the effects of the three chemical agents on the tensile strength (state clearly all constraints/assumptions). Explain all the terms in your model and estimate ALL the parameters. (e) Now repeat what you did in part (c) with the usual test for the same hypotheses based on the parametric model in part (d) and compare the P-values and conclusions of the two tests