課程名稱︰工程統計學 課程性質︰必修 課程教師︰周家蓓 教授 開課學院：工學院 開課系所︰土木工程學系 考試日期（年月日）︰2010-01-12 考試時限（分鐘）：120分鐘 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : ENGINEERING PROBABILITY AND STATISTICS Final Exam (1/12/2010) 1. (25%) In a certain type of metal test specimen, the normal stress on a specimen is known to be functionally related to the shear resistance. The following is a set of coded experimental data on the two variables. Normal stress,x Shear resistance,y ---------------------------------------------- 26.8 26.5 25.4 27.3 28.9 24.2 23.6 27.1 27.7 23.6 23.9 25.9 24.7 26.3 28.1 22.5 26.9 21.7 27.4 21.4 22.6 25.8 25.6 24.9 (a) Estimate the regression line y=α+βx (b) Estimate the shear resistance for a normal stress of 24.5 kilograms per square centimeter (c) What's the R square of this regress equation 2. (20%) One experiment would like to test the caffeine content of two brands of chocolates. The data are as following. Assume these two brands chocolates have the same variance and both normally distributed A brand B brand Sample no. 10 8 Sample mean 3.1% 2.7% Sample St. dev. 0.5% 0.7% (a) The 95% confident interval of mean difference (b) Set α=0.05, please test the H0: μ1-μ2 = 0 vs. H1: μ1-μ2≠0 3. (15%) A fuel oil company claims that one-fifth of the homes in a certain city are heated by oil. Do we have reason to doubt this claim if, in a random sample of 1000 homes in the city, it is found that 136 are heated by oil? Use a P-value in your conclusion. 4. (20%) (a) What are the definitions of α error and β error in the hypothesis test? (b) How do you control these two errors? (c) What is the meaning of P-value? (d) What is the power of a test? What are the key factors that affect the power of a test? 5. (20%) (a) How do you use Chi-square to test the goodness-of-fit? (b) Show that S^2 is an unbiased estimator of the parameter σ^2. ☆Extra Problem 6. (學期總成績加0~3分) Please write an International "Statistics Statement" which happened recently. (全卷完) -- --

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