1) The 2008 Olympics were full of controversy about new swimsuits possibly providing unfair advantages to swimmers, leading to new international rules that came into effect January 1, 2010, regarding swimsuit coverage and material. Can a certain swimsuit really make a swimmer faster? A study tested whether wearing wetsuits inuences swimming velocity. Twelve competitive swimmers and triathletes swam 1500 m at maximum speed twice each, once wearing a wet suit and once wearing a regular bathing suit. The order of the trials was randomized. Each time, the maximum velocity in meters/sec of the swimmer (among other quantities) was recorded. Here is the data: Swimmer 1 2 3 4 5 5 7 8 9 10 11 12 5,, s ' ---------IIEIIEI a) Explain why we want to analyze this data using statistical methods for paired data. b) Is this an experiment or an observational study? Explain. c) Why were the order of the swims randomized for each swimmer? d) Perform an appropriate statistical test to test whether the average maximum velocity for competitive swimmers differs when wearing wetsuits vs not wearing wetsuits. e) If you made an error in your conclusion, what type of error did you make? t) Suppose you wish to compute a 95% condence interval for the difference in average maximum velocity for competitive swimmers when wearing wetsuits vs not wearing wetsuits. What interval will you produce? g) Assume any necessary conditions are met (you already checked them, right?!), give the confidence interval and share it with a sentence. h) What is the t* for your 95% condence interval? i) What is the margin of error for your confidence interval? j) If you produced a 90% condence interval instead, would it be narrower or wider than the 95% interval? Explain. 2) Use a t-distribution to find a 95% confidence interval for the difference in means u 1 - 1.12 using this information from paired data: 59: 3.7, 3%: 2.1, "9d: 30. Give the best estimate for 1.1 1 1.12, the margin of error, and the confidence interval. Assume these results come from a random sample from a population that is approximately normally distributed