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 3 week period between rounds ensured that the sugars (oligofructose and sucrose) had been completely excreted before the second round commenced. The calcium absorption data are available in two data files, Oligo_paired.cov and Oligo_indep.cav. Only one of these is appropriate to the problem, and the same calcium absorption measurements appear in each file. 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 two calcium absorption measurements from a single subject In Oligo_indep.cav, the columns are headed "CaAbsorb" and "pill". CaAbsorb contains calcium absorption measurements, and "Pill" indicates whether the pill being taken before each measurement was a placebo or oligofructose. (a) [Note: this part is worth 4 marks because it is important to the rest of the question, not because it needs a long answer. A correct answer can be quite short. 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. [4] (b) provide a graphical display of the data, consistent with 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 a = .05. [12] END OF ASSIGNMENT