A commercial airline is considering four different designs of the control panel for the new generation of airplanes. To see if the designs have an effect on the pilot’s response time to emergency displays, emergency conditions were simulated and the response times, in seconds, of 8 pilots were recorded. The same 8 pilots were used for all four designs. The order in which the designs were evaluated was randomized for each pilot. The data are given in PilotReacTimes.txt.

(a) Write a model for the observations Xij and specify which parameters represent the treatment effects and which represent the random block effects.

(b) Using parameters of the model you wrote in part (a), state the null and alternative hypotheses relevant for deciding if the designs differ in terms of the pilot’s mean response time.

(c) Using R commands, perform the tests for checking the assumptions of homoscedasticity and normality of the intrinsic error variables of the model in (a). Report the p-values of the tests, and construct the residual boxplot and Q-Q plot. Comment on the validity of the two assumptions on the basis of the p-values and the plots.

(d) Regardless of the conclusions reached in part (c), carry out the ANOVA F procedure at level of significance α = 0.01 for testing the hypothesis in part (b), and report the p-value.