Final Exam - Short Questions - Probability Statistics Engineering Science | MATH 390, Exams of Mathematics

Download Final Exam - Short Questions - Probability Statistics Engineering Science | MATH 390 and more Exams Mathematics in PDF only on Docsity! STAT/MATH 390 —– SUMMER 2001 Final Examination Name: Student ID: Section: • Please print your name, student ID and your quiz section in the above spaces. • Do not open the exam until instructed to do so. • This is a closed book examination. You may use your calculator and you may use the sheet of formulae you have written. Notes, textbook and homeworks are not permitted. • To receive full credit for a problem, you must show it clearly how you arrived at your answer. • Extra paper will be provided if you need it. Please write your name on any extra paper used and clearly label the problems answered on the extra paper. • This examination consists of 5 problems. Please make sure that your test paper is complete. • Good luck. 1 1. (20 points) Answer the following short questions (a) (5 points) State the assumptions of two-sample t test. (b) (5 points) In hypothesis testing, why we sometimes choose α = 0.05, while α = 0.01 can also be employed? (c) (5 points) Suppose a study reports that “With 90% confidence, Alaska husbands are -0.5 to 4.3 years older than their wives.” Is there statistical evidence that the mean age of (Alaska) husbands is greater than the mean age of their wives? Why? (d) (5 points) Referring to above statement, what is the point estimate for the differ- ence in ages, and the bound on the error of estimation (or margin of error)? 2 (b) (8 points) Does this data suggest that the true surface pH appear to be different from the true subsoil pH? Carry out a test of appropriate hypotheses using α = 0.01. Be sure to state any assumptions necessary for your analysis. (c) (5 points) We discussed in class the relationship between confidence intervals and hypotheses tests. Describe how your results in (a) and (b) are either consistent or inconsistent with what we should expect. 5 4. (20 points) In an experiment to investigate the performance of four different types of spark plugs intended for use on a two-stroke motorcycle, five plugs of each brand were tested and the number of driving miles ( at a constant speed) until plug failure was recorded. A partial ANOVA table for this data follows: Sources of Variation df SS MS F Brand Error 14713.69 Total Variation 310500.76 (a) (10 points) Fill in the missing entries in the ANOVA table. (b) (5 points) State the null and alternative hypotheses of interest in this experiment. (c) (5 points) Use α = 0.05 to carry out the hypothesis test in part (b). 6 5. (20 points) The paper “Refuse-Derived Fuel Evaluation in an Industrial Spreader- stoker Boiler” (J. Engr. for Gas Turbines and Power, 1984, pp 782-788) reports the accompanying data on x = % refuse-derived fuel (RDF) heat input and y = % efficiency for a certain boiler: x 37 30 48 29 27 16 0 20 y 78.0 77.2 74.4 77.7 76.9 79.0 82.1 76.5 The following computations might be useful in solving the problem: 8∑ i=1 xi = 207, 8∑ i=1 yi = 621.8, 8∑ i=1 y2i = 48363.76, 8∑ i=1 x2i = 6799, 8∑ i=1 xiyi = 15896.8. (a) (6 points) Obtain the equation of the estimated regression line. (b) (6 points) What proportion of the observed variation in % efficiency for a certain boiler can be explained by the model relationship. 7