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IEOR 165 Homework 2 Due March 5, 2015 Electronic copies will not be accepted except under extenuating circumstances. Each student must turn in their own homework solutions. Question 1. A randomized, double-blind experiment was conducted to assess if the several drugs for reducing postoperative nausea are effective more than 50 percent of the time. The data are as follows. Chlorpromazine Dimenhydrinate Pentobarbital (100 mg) Pentobarbital (150 mg) Number of Patients 100 120 110 330 Incidence of Nausea 58 73 63 185 a. Test the hypothesis that the proportion of incidence of nausea is 50% at the 5 per cent level. b. Use the Bonferroni to adjust for multiple testing. c. Use the Bonferroni-Holm to adjust for multiple testing. Question 2. The following data relate to the ages at death of a certain species of rats that were fed 1 of 3 types of diets. Thirty rats of a type having a short life span were randomly divided into 3 groups of 10 each. The sample means and variances of ages at death (in months) are: Sample mean Sample variance Very Low Calorie 22.4 24.0 Moderate Calorie 16.8 23.2 High Calorie 13.7 17.1 a. Test the hypothesis, at the 5 percent level of significance, that the mean lifetime of a rat is not affected by its diet. b. Repeat assuming the numbers in the groups were 5 for very low calorie, 10 for moderate, and 15 for high calorie. c. For the original data, compute the joint 95% CI for the three means. Hint: Use the Bonferroni correction. 1 Question 3. Assume that items produced are supposed to be normally distributed with mean 35 and standard deviation 3. To monitor this process, subgroups of size 5 are sampled. If the following represents the averages of the first 20 subgroups, does it appear that the process was in control with significance level 0.05? Subgroup No. X̄ Subgroup No. X̄ 1 34.0 11 35.8 31.6 12 35.8 2 3 30.8 13 34.0 4 33.0 14 35.0 5 35.0 15 33.8 6 32.2 16 31.6 33.0 17 33.0 7 8 32.6 18 33.2 9 33.8 19 31.8 10 35.8 20 35.6 Question 4. Suppose we would like to use an exponentially weighted moving-average control chart for data that should come from N (µ = 5, σ 2 = 2). Assume the subgroup size is n = 10, and that we have chosen γ = 0.2. Use a Monte Carlo algorithm to determine the value of α so that the expected number of subgroups that are analyzed before the process is determined to be out of control (in the case where the process never goes out of control) is 1000. Return your results and code. 2