are used to inoculate the gut of 20 gnotobiotic (germ-free) mice, 10 with each separate community The gut microbial community from an obese and a lean mouse are harvested for subsequent transplantation. These two communities. After two weeks the increase in body fat of the mice and energy content of fecal samples are measured.
a) State the two possible hypotheses about the possible outcomes of this experiment. Frame this in the context of statistical significance.
b) The following results were obtained:
S1: Mice with microbial community from obese source
S2: Mice with microbial community from lean source
Bomb calorimetry of the faecal gross energy content (kcal g-1)
S1 =[3.2316, 3.1642, 3.0398, 3.0568, 3.0186, 3.0991, 3.0324, 2.9469, 3.1815, 3.1593]
S2 =[3.2661, 3.1444, 3.4979, 3.8173, 3.3540, 3.4254, 3.4319, 3.7482, 3.5888, 3.3160]
Increase in total body fat (%)
S1 =[34.7751, 82.0402, 66.8450, 28.6254, 111.9754, 86.4072, 14.9222, 39.1467, 49.1888, 81.6303]
S2 =[34.2439, 36.3036, 32.3342, 24.2585, 42.9152, 45.0858, 34.7660, 27.5398, 32.4703, 25.1005]
Determine the sample means and variance. Plot the t-distributions for the sample means given the statistics you calculate.
Use two-tailed unpaired t-tests to determine whether the source of the gut flora inoculums made a difference. i.e. compare the two sets of data for each measured quality: faecal gross energy content and increase in total body fat. Use a level of significance of 0.05 and assume that the quantities are normally distributed.
c) What are the P-values for the two different sets of data? Provide an explanation for what these P-values mean in each case.
d) What is another potential quality of the mice to test?