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A rehabilitation center researcher was interested in examining the relationship between physical fitness prior to surgery of persons undergoing corrective knee surgery and time required in physical therapy until successful rehabilitation. Participant record in the rehabilitation center were examined, and 24 male subjects ranging in age from 18 to 30 years who had undergone similar corrective knee surgery during the past year were selected for the study. The number of days required for successful completion of physical therapy and the prior physical fitness status (below average, average, above avenge) for each patient follow. Assume that ANOVA model ( 16.2 ) is appropriate. a. Prepare aligned dot plots of the data. Do the factor level means appear to differ? Does the variability of the observations within each factor level appear to be approximately the same for all factor levels? b Obtain the fitted values. c. Obtain the residuals, Do they sum to zero in accord with (16.21)\(?\) d. Obtain the analysis of variance table e. Test whether or not the mean number of days required for successful rehabilitation is the same for the three fitness groups. Control the \(\alpha\) risk at. \(01 .\) State the alternatives, decision rule, and conclusion f. Obtain the \(P\) -value for the test in part (e). Explain how the same conclusion reached in part (e) can be obtained by knowing the \(P\) -value. g. What appears to be the nature of the relationship between physical fitness status and duration of required physical therapy?