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Unformatted text preview: Stat 5102 (Geyer) Spring 2012 Homework Assignment 5 Due Wednesday, February 29, 2012 Solve each problem. Explain your reasoning. No credit for answers with no explanation. If the problem is a proof, then you need words as well as formulas. Explain why your formulas follow one from another. 5-1. In each of the situations below explain whether a one-tailed or a two- tailed test is more appropriate. If you can’t tell, give arguments for both sides. (a) Two groups are considered independent samples from the population of interest. One is given a treatment for pain, the other is given a placebo, which looks and feels like the treatment, but does not contain the active ingredient and hence should not work. The response is a quantitative measure of each individuals report of pain relief. The response will be considered approximately normal and a two-sample t test done. (b) Same as above, except there is no placebo. Two active treatments are compared. One is aspirin; the other is a new medication being consid- ered for approval. (c) Same as above, except the two active treatments being compared are both new. 5-2. Suppose the following data- . 33 3.52- . 08 3.36 7.26 3.56 7.46 7.14 3.73 4.64 0.05 1.06 5.81 3.04 are differences between treatment and control in a paired comparison exper- iment. We wish to test the null hypothesis that unknown true difference of population means is zero using an upper-tailed test. (a) Perform a t test and interpret the P-value. (b) Perform a sign test and interpret the P-value. (c) Perform a signed rank test and interpret the P-value. If you want to use R on this problem, the data are in the file http://www.stat.umn.edu/geyer/5102/data/prob5-2.txt 1 5-3. Two groups in physics lab have been measuring the density of alu- minum at room temperature (20 ◦ C). They got the following summary statis- tics n X n S n Group I 10 2.792 0.241 Group II 8 2.538 0.313 (Units are grams per cubic centimeter.) Assume the measurements for group(Units are grams per cubic centimeter....
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- Normal Distribution, Statistical hypothesis testing, Yi, 0.10 inches, 0.28 inches