[6] 5. You've conducted a study to determine whether the activity levels of 20 genes have changed in a group of subjects who have switched from a vegetarian diet to a vegan diet for 10 days. For each gene, a hypothesis test was conducted with a null hypothesis of no difference in activity, and an alternative hypothesis that the difference in activity levels is non-zero. A significance threshold of a = 0.05 was used for each of these tests. The p-values of these tests, in ascending order, were: 0.0013, 0.052, 0.058, 0.06, 0.24, 0.36, 0.45, 0.48, 0.61, 0.7, 0.71, 0.72, 0.74, 0.82, 0.84, 0.89, 0.91, 0.91, 0.95, 0.98 [1] (a) If the null hypotheses (of no difference) were actually true for all twenty of these genes, how many false positive findings would be expect, on average, if we used a significance threshold of 0.05? [1] (b) If the null hypotheses (of no difference) were actually true for all twenty of these genes, what is the probability that one or more of these tests would result in a false positive if we used a significance threshold of 0.05? [1] (c) How many of the genes in this study showed statistically significant evidence for a non-zero change in activity levels, using a significance threshold of 0.05? 2] (d) Use the Bonferroni adjustment to determine a new p-value threshold that will control the Family Wise Error Rate for these twenty genes at a level of 0.05. How many genes achieve statistical significance if we use this adjusted threshold? [1] (e) Consider the list of genes that achieve statistical significance using the Bonferroni- adjusted cut-off you determined in part d). According to the definition of the Bon- ferroni correction, what is the probability that one (or more) of the genes in this list are false positives