Question 1) Suppose that you work for a company that is marketing a new weight loss supplement. You would like to run an advertisement that claims that your supplement helps people lose an average of more than 15 pounds. To study this you gather 11 random adult subjects, measure their weight in pounds, then give them the supplement for 6 weeks and measure their weight again in pounds. (Note: You may assume there were lots of adults to choose from) You get the following data: Subject Weight BEFORE Weight AFTER 285 278 2 305 295 3 240 224 4 195 173 5 264 241 6 353 339 7 205 188 8 278 252 9 291 274 10 300 282 11 296 281 (Questions on next page) 1 (a) Carry out a hypothesis test at a = .05 to test your claim that people can lose more than 15 pounds on average using your supplement. Make sure to check all necessary conditions and state your conclusion in the context of this problem. (b) Build a 95% confidence interval for the average weight loss that come from using this weight loss supplement. Make sure to interpret your interval. (c) If you decided there was not enough evidence to run your ad that your supplement helps people lose more than 15 pounds on average when in reality it does help people lose more than 15 pounds on average, would this be a Type I or Type II error? EXTRA CREDIT QUESTION: In part (a) of Question 1 you confirmed that the differences looked approximately normal. This means you could apply the empirical rule to this data. Use the empirical rule to build an interval that would capture 95% of the INDIVIDUAL weight losses from your supplement. How does this interval compare to your 95% confidence interval you built in (b)