(1)What design (within or between subject) and statistical test (t-test, KS test, ANOVA, Z-test, Chi-Squared test) would you use in each of these scenarios? If you use ANOVA, you need to mention whether you will use a one way or two-way ANOVA.

(a)You want to find out which of the five different designs of an e-commerce website are more persuasive at making consumers buy goods. You want to test these five designs on set of 1000 customers for each of whom you would show one version of the site and then measure how much they spent on products on the site. What is the design and statistical test you would use for this?

(b)Smokers are of four types: Non-Smoker, Light Smoker, Medium Smoker and Heavy Smoker. Drinkers are of three types:Non-Alcoholic, Light Drinker, Heavy Drinker.You want to test the effect of smoking and drinking on the body weight. You have a set of 30 people in each of the possible combinations of smoking and drinking. (0.5 Points)

(c)You want to test the impact of being Vegan, Vegetarian and Non-Vegetarian on changes to body weights of a set of 30 people. You have a set of 30 people who are non-vegetarian and you ask them to be vegans for 3 months and measure the changes in their body weights. You then ask them to be vegetarian for another 3 months and measure their changes in body weight. Finally, you let them be non-vegetarian and measure their changes in body weight after 3 months again. What design and statistical test would you use? (0.5 Points)

(d)You want to know which of drugs A, B, C are more effective at reducing blood pressure.You administer each of drugs A, B and C to a set of 30 different patients each and observe the reduction in blood pressure after 3 months. (0.5 Points)

(e)In case of part (d), if you want to test if the distributions of the differences in reduction in blood pressure is the same for drugs A and B, what test would you use?(0.5 Points)