Random samples of 100 persons awaiting trial on felony charges were selected from rural, urban, and suburban court locations in each of two states, one (state 1) in the Northeast and the other (state 2) in the South. The following table summarizes the data on the time Y (in months) between arrest and beginning of trial for these random samples.

a. Do the sample means in the table suggest that the average waiting times for state 1 vary by courr location differently from how they vary for state 2? Is there an interaction effect?
b. Analyze these data. Use the following ANOVA table. Assume that both factors are fixed.

c. Define an appropriate regression model for this two-way ANOVA.
d. How might one revise the model in part (c) and the associated ANOVA table in order to investigate whether a linear trend exists between waiting time and degree of urbanization (as determined by treating the categories rural, suburban, and urban on an ordinal scale)? What difficulty does one encounter when considering such a model?

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Court Location State Rural Suburban Urban Y-5.8,S 1.2 Y 3.5, S 1.7 y-3.4,S 1.3 6.8, 1.5 Y 4.7, S 1.7 d.f. MS SourcC States Court locations Interaction Error 486.00 826.33 49.00 1,327.591 486.00 413.17 24.50 594 2.235