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Unformatted text preview: CE93 – Engineering Data Analysis Prof. Joan Walker, Spring 2011 Assignment #12 – Final Exam Review: “Due” May 4 th , 2011 (This assignment will not be graded. Solutions will be posted on due date) Note: This final exam review can be treated as a practice test – it is to your benefit to attempt this assignment in the conditions of the actual final exam (i.e. no MATLAB, crib sheet only, etc.) Problem #1 The structural soundness of aircraft is determined using alignment checks, which involve measuring distances between different points on the aircraft and comparing them with specifications. When a measurement is outside of a prescribed tolerance, it is termed an “alignment error.” The number of alignment errors is related to the number of missing rivets on the aircraft. Data for four aircraft is presented below. Number of Missing Rivets, x Number of Alignment Errors, y 13 7 15 7 10 6 22 12 From the above data, the following quantities were calculated: ? = 15 ? ¡ = 8 ¢ ? = 5.1 ¢ ? = 2.7 £ ? ? 2 4 ? =1 = 978 £ ? ? 2 4 ? =1 = 278 £ ( ? ? − ? 4 ? =1 ) 2 = 78 £ ( ? ? − ? ¡ 4 ? =1 ) 2 = 22 £ ( ? ? − ? 4 ? =1 ) ∗ ( ? ? − ? ¡ ) = 40 a) What are the OLS estimates of the slope ( ¤ ) and intercept ( ¥ ) of the regression line relating x and y? Show your calculations. b) Estimate the variance of the residual of this model. c) How would you measure the “fit” of the OLS equation to your data? Perform the calculation. d) What is the 95% confidence interval for the slope? e) Test the hypothesis that ¤ = 0.5 against the alternative hypothesis that ¤ ≠ 0.5 , using a significance level of 0.05. CE93 – Engineering Data Analysis Prof. Joan Walker, Spring 2011 Problem #2 An aircraft is carrying 200 passengers and their baggage. The aircraft has sufficient fuel, without refueling, for its next leg if its total payload (weight of passengers and their baggage) is less than 50,000 lb. The weights of five passengers and their bags are measured, and found to be 200, 220, 150, 170, and 260 lbs respectively. Assume that weights of passengers on this aircraft follow a normal distribution....
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- Spring '08
- Normal Distribution, Probability theory, Engineering Data Analysis, Prof. Joan Walker