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#1. GoodDrug, manufactured by GoodPharma, is a drug used for treating each chronic point pain. An to advertisement one study subject, for this X drug is the included "pain intensity a scatterplot on pre-study of (x,y) points, OldDrug where program" and the y published corresponds is the "pain intensity after 1 month on GoodDrug". The values listed below are based on scatterplot, and the y values corresponds to the respective X values. X: .2; 1.3; 1.5; 1.6; 8.1; 3.4; 3.5; 2.8; 2.6; 2.2; 3.0; 7.1;2.3; 2.1; 3.4; 6.4; 5.0; 4.2; 2.8; 3.9; 5.2; 6.9; 6.9; 5.0; 5. .5; 6.0; 5. 5; 8.6; 9.5; 10.0; 7.6 y: 0.4; 1 4; 1 8; 2.9; 6. .0; 1 .4; 0.7;3.9; 0.9; 1.9; 0.9; 9.3; 9.0; 6.8; 2.3; 0.4; 0.7; 1.2;4.5; 2.0; 1.6; 2.0; 2.0; 6.8; 6.6; 4.1; 4.6; 2.9; 5.4;4.8; 4. 1 (a) Is there any linear correlation between the pre-study and after-one-month pain intensity? (use a = 0.01) 3 points (b) Find the equation of the regression line. Would you use this equation to predict the outcomes based on the pre-study pain intensity data (please explain)? 3 points (c) Identify the equation of the line corresponding to a drug that has absolutely no effect. 4 points (d) Modify the regression line equation determined in (b) to an upward opening parabola. Plot the curve and predict y for X = 8.1, 1.7, and 3.2.2 points #2. A correlation between mental and physical well-being has increasingly become accepted. An analysis of "big event" in a family (e.g. a new grandson/daughter) and death days of aged people could be used as further evidence of the study of this correlation. If an aged person is in poor health and dying, then perhaps expecting the "big event" would cheer him up and consequently improve his health and lowering the chance that he will die shortly before his birthday. The data would then indicate that an aged person is less likely to die in the months before the "big event" and more likely to die in the months after the event. Test this hypothesis using the data below: 5 points 6 5 4 3 2 1 The 1 2 3 4 5 6 month month month month month month month month month month month month month before before before before before before after after after after after after N of 90 100 87 96 102 86 119 118 118 122 114 113 106 death #3. The birth weights (in pounds) of n = 8 pairs of identical twins are recorded, where X represents the weight of the firstborn and Y represents the weight of the second born twin: X 5.50 6.06 6.94 5.00 4.89 5.94 5.31 5.31 5.94 Y 5.06 6.02 6.75 5.06 4.75 5.51 5.00 5.00 4.88 (a) Assuming that = 5.3 and O = 0.5 are predetermined firstborn twin population mean and standard deviation values, estimate minimum sample size required to show that the firstborn twin's weight is greater that the one of the second born twins with the difference in mean d = 0.35. Use a = 0.1 and ß = 0.2. 3 points (b) Using = 0.3, test the doctors' claim that firstborn twin weights is equivalent to the second born twin weights. 4 points (c) The Bright Future Hospital doctors strongly believe that firstborn twins have mean weight value X = 4.1 with standard deviation 0.3 and claim that the obtained sample mean and standard deviation values are overestimated and have to be corrected. What is the sample mean according to the Bright Future Hospital doctors? Test the claim that the sample mean is different from the reference number given in (c). 4 points #4. A physiologist investigated the effect of three different patterns of reward (RR = full reinforcement, RU = reinforcement trial followed by unreinforcement trial, UR = unreinforcement trial followed by reinforcement trial) upon extent of learning an opposing habit. Eighteen litters of rats, three in each litter, were trained under the three patterns of reward, and the three rats in each litter were randomly assigned to the three reinforcement patterns. The extent of learning was measured by counting the number of errors made in the trials to compare the three reward patterns. The error counts are ranked within each litter. Is there any effect of the reinforcement pattern? Perform the test at 5% significance level and interpret the data. 5 points 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 RR 1 2 1 1 3 2 3 1 3 3 2 2 3 2 2.5 3 3 2 RU 3 3 3 2 1 3 2 3 1 1 3 3 2 3 2.5 2 2 3 UR 2 1 2 3 2 1 1 2 2 2 1 1 1 1 1 1 1 1 #5. A purification process for a chemical involves passing it, in solution, through a resin of 3 on which impurities are absorbed. A chemical engineer wishing to test the efficiency different resins took a chemical solution and broke it into 30 batches. She tested each resin 5 times and then measured the concentration of impurities after passing though the resins using two different temperature regimes. Her data are shown below. Is there any interaction between temperature and type of the resin? In there sufficient evidence to support the claim that the temperature regime has an effect on concentration of impurities? Is there sufficient evidence to support the claim that the type of resin has an effect on concentration of impurities? 5 points Concentration of Impurities Resin | Resin Il Resin III 0.046 0.038 0.031 25oC 0.025 0.035 0.042 0.014 0.031 0.02 0.017 0.022 0.018 0.043 0.012 0.039 0.048 0.037 0.031 0.027 10oC 0.036 0.042 0.016 0.030 0.02 0.019 0.021 0.018 0.045 0.011 0.039

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