课程名称︰工程统计学 课程性质︰必修 课程教师︰周家蓓 教授 开课学院：工学院 开课系所︰土木工程学系 考试日期（年月日）︰2010-01-12 考试时限（分钟）：120分钟 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 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. (学期总成绩加0~3分) Please write an International "Statistics Statement" which happened recently. (全卷完) -- --

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