3. [20 marks] A double-blind randomised experiment investigated whether consumption of oligofructose would stimulate calcium absorption in healthy human males aged 14 to 16 years. Two sets of pills were prepared, identical in appearance and packaging. One set contained oligofructose and the other set contained ordinary sucrose (i.e., a placebo). The experiment ran in two rounds, with the second round starting 3 weeks after the first ended. Subjects were randomly assigned to either receive oligofructose in the first round and the placebo in the second, or the placebo in the first round and oligofructose in the second. In each round, subjects took pills for nine days and had their calcium absorption measured on the last day. Calcium absorption was measured as a percentage of calcium intake. The calcium absorption data are available in two data files, Oligo_paired.csv and Oligo_indep.csv. The measurements in each file are the same, but only one of these files is appropriate to the problem. In Oligo_paired.csv, the data columns are headed "Placebo" and "Oligofructose" to indicate which pill was being taken when calcium absorption was measured. Each row contains calcium absorption measurements from a single subject. In Oligo_indep.csv, the columns are headed "CaAbsorb" and "Pill". CaAbsorb contains calcium absorption measurements, and "Pill" indicates whether the pill being taken was a placebo or oligofructose. (a) [Note: this part is worth 5 marks because it is important to the rest of the question, not because it needs a long answer. A correct answer need not be very long. Follow-through marks will be available if you get this part wrong.] Should the data be analysed as independent samples, or as paired data? Justify your answer. [5] (b) Provide a graph of the data distribution appropriate to your choice of analysis. [4] (c) Formally test whether oligofructose stimulates calcium absorption in healthy males aged 14 to 16 years. You do not need to revisit the decision made in part (a), but your report should be consistent with that decision, and should include all relevant elements of a hypothesis test. Assume ? = .05. [11]

\fPlacebo Oligofructose 1 68.4 72.0 2 66.6 85.1 3 57.4 56.5 4 51.5 59.4 5 49.0 79.7 6 46.6 53.8 7 44.2 60.3 8 42.9 61.6 9 37.2 76.6 10 34.1 62.7 11 24.6 64.0CaAbsorb Pill 1 68.4 Placebo 2 66.6 Placebo 3 57.4 Placebo 4 51.5 Placebo 49.0 Placebo 6 46.6 Placebo 7 44.2 Placebo 8 42.9 Placebo 9 37.2 Placebo 10 34.1 Placebo 11 24.6 Placebo 12 72.0 Oligofructose 13 85.1 Oligofructose 14 56.5 Oligofructose