4. The data file AdhesHumTemp.txt contains simulated data from a study conducted to investigate the effect of temperature and humidity on the force required to separate an adhesive product from a certain material. Two temperature settings (20◦, 30◦) and four humidity settings

(20%, 40%, 60%, 80%) are considered, and three measurements are made at each temperature-humidity combination. Let μij denote the mean separating force at temperature-humidity combination (i, j).

(a) The experimenter wants to know if the difference in the mean separating forces between the two temperature levels is the same at each humidity level. In statistical notation, of interest is whether

is false.Which is the relevant hypothesis to be tested?

(b) The experimenter wants to know if the average (over the two temperature settings) of the mean separating forces is the same for each humidity setting. In statistical notation, of interest is whether

is false.Which is the relevant hypothesis to be tested?

(c) Test for no interaction and for no main effects for each of the two factors. Report the three test statistics and the corresponding p-values, and state whether each of the three hypotheses is rejected at level of significance 0.05.

(d) Is it appropriate to conduct multiple comparisons for determining which of the humidity level main effects are different from each other? If so, perform the multiple comparisons at level of siginficance 0.01, and state your conclusions.

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