Suppose that 18 obese subjects were randomized, 9 each, to a new diet pill and a placebo. Subjects' body mass indices (BMis) were measured at a baseline and again after having received the treatment or placebo for four weeks. The average difference from follow-up to the baseline (follow-up - baseline) was 3kg/m2 for the treated group and 1kg/m2 for the placebo group. The corresponding standard deviations of the differences was 1.5kg/m2 for the treatment group and 1.8 kg/m2 for the placebo group. The study aims to answer whether the change in BM1 over the fourweek period appear to differ between the treated and placebo groups. What is the pooled variance estimate? (to 2 decimal places) Suppose that in an AB test, we test two website design for an online retailer. The first design leads to an average of 10 purchases per day for a sample of 100 days, while the other leads to 11 purchase per day, also for a sample of 100 days. Assuming a common standard deviation of 4 purchases per day. If the groups are independent and the days are independent and identically distributed, calculate the z test statistics. Give the p-value for the test. Do you reject at the 5% level? Write the R code to find the probability of 2 heads in 10 coin flips where probability of heads is 0.3