12.55 Financial incentives for weight loss. The use of financial incentives has shown promise in promoting weight loss and healthy behaviors. In one study, 104 employees of the Children’s 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.15 Participants in the control program were provided 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 of five and at the end of each four-week period, those in their group that 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.

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FIGURE 12.19 Residual plot and Normal quantile plot, Exercise 12.53.
  1. (a) Make a table giving the sample size, mean, and standard deviation for each group.

  2. (b) Is it reasonable to pool the variances? Explain your answer.

  3. (c) Generate a histogram for each of the programs. Can we feel confident that the sample means are approximately Normal? Defend your answer.