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Exam2Sp2011_key - KEY Stat 205 Exam II Write clearly and...

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KEY Stat 205 Exam II Write clearly and show steps for partial credit. This exam is open book. There are five problems. 1. (30 points) Androstenedione is a steroid that is thought by some athletes to improve strength. Researchers investigated this claim by giving androstenedione to one group of men and a placebo to a control group of men. One of the variables measured in the experiment was the increase in “lat pull-down strength” in pounds of each subject after four weeks; a lat pull-down is a type of weight lifting exercise. The Welch-Satterthwaite approximation gives 16.5 degrees of freedom. The data are summarized in the following table. Andro Control n 10 9 ¯ y 20.0 14.4 s 12.5 13.3 (a) The researchers want to show that androstenedione improves strength. Carefully define μ 1 and μ 2 and state the appropriate null and alternative hypotheses for this experiment. ANSWER μ 1 is the mean increase in lat-pull down weight (lbs) for the population taking androstenedione and μ 1 is the mean increase in lat-pull down weight for those that are not. The experimenters want to test H 0 : μ 1 = μ 2 versus H A : μ 1 > μ 2 . That is, they want to show that androstenedione increases the average amounnt of weight lifted. (b) Find the standard error SE ¯ y 1 - ¯ y 2 . ANSWER SE ¯ y 1 - ¯ y 2 = s 2 1 n 1 + s 2 2 n 2 = 12 . 5 2 10 + 13 . 3 2 9 = 5 . 94 lbs. (c) Find the test statistic t s . ANSWER t s = ¯ y 1 - ¯ y 2 SE ¯ y 1 - ¯ y 2 = 20 . 0 - 14 . 4 5 . 94 = 0 . 94 .
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