QUESTION 1 [10 MARKS] Suppose we suspect an unusual distribution of blood groups in patients undergoing one type of surg

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Question 1 10 Marks Suppose We Suspect An Unusual Distribution Of Blood Groups In Patients Undergoing One Type Of Surg 1 (210.17 KiB) Viewed 78 times

QUESTION 1 [10 MARKS] Suppose we suspect an unusual distribution of blood groups in patients undergoing one type of surgical procedure at a certain hospital. We know that the expected distribution for the population served by the hospital which performs this surgery is 44% group 0, 45% group A, 8% group B and 3% group AB. The table below shows the blood grouping results of a random sample of 187 consecutive patients. O A B AB Blood group Number of patients 67 83 29 8 Test, at 1% level of significance, whether the distribution of blood groups of this random sample is significantly different from the expected distribution of blood groups. [10] QUESTION 2 [20 MARKS] The mechanical engineer wishes to determine whether the tread wear of a newly developed brand of tires is affected by the speed of automobile controlling for the supplier of the rubber material used to make these tires. The following data were observed. Speed Slow Medium Fast Total A 3.7 4.5 3.2 11.4 Supplier of rubber material B C D 3.4 3.8 3.5 3.9 4.8 4.2 2.9 3.1 3.4 10.2 11.7 11.1 Total 14.4 17.4 12.6 44.4 (a) Construct an appropriate ANOVA table for these data. [12] (b) Test whether the tread wear is affected by the speed of automobile and/or the supplier of the rubber material at 0.1% significance level. [8] QUESTION 3 (25 MARKS) A researcher is interested in predicting value of variable Y given the value of variable X. Suppose that she has observed the data given in the table below. 6 7 8 X Y 4 540 5 330 9 52 200 130 85 Page 2 of 4 One best fitting model for these data is a simple nonlinear model of the form Y = ABX where A and B are constants. (a) State any 4 assumptions of a simple linear regression model. [4] (b) Transform the given simple nonlinear model into a simple linear model. [3] (c) Use the ordinary least squares (OLS) method to fit the transformed simple linear model. [All transformed data must be rounded to 2 decimal places). [10] (d) Use the fitted model in 3 (b) to predict the value of Y when X = 8.25. [3] (e) Given that the standard error of estimate for the transformed linear regression is 0.0269, construct the 95% confidence interval for B in the original nonlinear model. [5]