In a study of the use of financial incentives for promoting weight loss,104employees of the Chil-drens Hospital of Philadelphia, with BMIs of 30 to 40 kilograms per square meter (kg/m2), were each randomly assigned to one of three weight-loss programs. Participants in the control program were pro-vided a link to weight-control information. Participants in the individual-incentive program received this link but were also told that $100 would be given to them each time they met or exceeded their target monthly weight loss. Finally, participants in the group-incentive program received similar information and financial incentives as the individual-incentive program but were also told that they were placed in secret groups of5and at the end of each4-week period, those in their group who met their goals throughout the period would equally split an additional $500. The study ran for 24 weeks and the total change in weight (in pounds) was recorded.

1. Obtain confidence intervals for all pairwise comparisons between the treatment means; use theTukey studentized range procedure and a95%family confidence coefficient. Interpret your results and provide a graphic summary.

wtloss Ctrl -7.1 Indiv 10.4 Group Loss Ctrl -9.9 Indiv -23.5 -2.5 Ctrl Grp 5.3 Ctrl -5.6 Indiv 8 Ctrl 15.5 Grp Ctrl 3.9 -1 Indiv -5.7 Ctrl 4.8 Grp 16.5 -2.2 Ctrl Indiv 0.5 Ctrl 6.1 Ctrl -14.9 Indiv -32.1 -2.1 Grp Ctrl -4.9 Ctrl -0.3 Indiv -5 Grp -30.5 Ctrl 6.1 Ctrl -4.3 Indiv -8.4 Grp -4.1 Ctrl 6.6 Ctrl -30.4 Indiv 0.2 Grp -18.1 Ctrl -4.5 Ctrl -12.5 Indiv 12 Grp -5.5 Indiv -6.8 Ctrl -15.4 Indiv -5.6 Grp -14.1 Indiv -4.8 Ctrl -19.5 Indiv -1.6 Grp -18.2 Indiv 5.5 Ctrl -6.5 Indiv -10.7 Grp -11 Indiv 11.9 Ctrl 13.4 Indiv -4 Grp -19 Indiv -9 Ctrl -4.2 Indiv -11 Indiv -4.7 Grp 3.1 Ctrl 6.9 Indiv -12.1 Indiv -9.1 Grp -12 Ctrl 25.5 Indiv -15.1 Indiv -15.1 Grp -24.4 Ctrl -0.3 Grp -11.4 Indiv -1.6 Grp -11.3 Ctrl -3.2 -7.3 Indiv -3.8 Grp Grp Grp 11.3 Ctrl 1.9 -19.8 Indiv 7.3 Grp -5.2 Ctrl -6.6 Grp -13.7 Indiv -6.3 Grp -12.9 Ctrl -12.7 Grp -9 Indiv 12.4 Grp -18.6 Ctrl -1.2 Grp -22.4 Indiv -0.9 Grp Ctrl 19.4 -13.7 -9.6 Grp Indiv -1.9 Ctrl Grp 14.3 Grp 1.1 -19.2 Indiv -18.3 Ctrl Grp 8.8 -2.6 -23.9 Grp Indiv 6.9 Ctrl 6.8 Indiv Grp Grp -19.6 -17.8 -0.4 ## Weight loss in three financial incentive groups ## (Ctrl, Indiv, Grp) wtloss