(b) Construct 95% (simultaneous) confidence intervals for the contrasts representing the number format effect, the parity type effect and the interaction effect. Interpret the resulting intervals. (c) The absence of interaction supports the M model of numerical cognition, while the presence of interaction supports the C and C model of numerical cognition. Which model is supported in this experiment? (d) For each subject, construct three difference scores corresponding to the number for- mat contrast, the parity type contrast, and the interaction contrast. Is a multivariate normal distribution a reasonable population model for these data? Explain. 6.18. Jolicoeur and Mosimann [12] studied the relationship of size and shape for painted tur- thes. Table 6.9 contains their measurements on the carapaces of 24 female and 24 male turtles (a) Test for equality of the two population mean vectors using a = .05. (b) If the hypothesis in Part a is rejected, find the linear combination of mean compo- nents most responsible for rejecting Ho. (c) Find simultaneous confidence intervals for the component mean differences Compare with the Bonferroni intervals. Hint: You may wish to consider logarithmic transformations of the observations. 6.19. In the first phase of a study of the cost of transporting milk from farms to dairy plants, a survey was taken of firms engaged in milk transportation. Cost data on X, = fuel. X2 = repair, and Xy = capital, all measured on a per-mile basis, are presented in Table 6.10 on page 345 for my = 36 gasoline and ny = 23 diesel trucks. (a) Test for differences in the mean cost vectors, Set a = .01. (b) If the hypothesis of equal cost vectors is rejected in Part a, find the linear combina- tion of mean components most responsible for the rejection. (c) Construct 99% simultaneous confidence intervals for the pairs of mean components. Which costs, if any, appear to be quite different? (d) Comment on the validity of the assumptions used in your analysis. Note in particular that observations 9 and 21 for gasoline trucks have been identified as multivariate outliers. (See Exercise 5.22 and [21.) Repeat Part a with these observations deleted