Aim 1 - between group analysis sample size
We power the multivariable analysis based on test for two means in a 2-level hierarchal design with level 2 randomization. Sample sizes of 96 subjects in each group, which were obtained by sampling 3 clusters with an average of 32 subjects per cluster, achieve >90% power to detect a difference between the group means of at least 5 minutes (or 5 percent difference in meeting recommended levels). A test based on a mixed-model analysis at a significance level of 0.05.