312-sample midterm4 and soln

Probability and Statistics for Engineering and the Sciences (with CD-ROM and InfoTrac )

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Stat312: Midterm Exam II. Moo K. Chung, Yulin Zhang [email protected], [email protected] November 11, 2004 Please use the following R output in answering the appropriate exam problems. > pnorm(c(1.0,1.1,1.2,1.3,1.4,1.5,1.6)) [1] 0.84 0.86 0.88 0.90 0.92 0.93 0.95 > pt(c(1.0,1.1,1.2,1.3,1.4,1.5,1.6),9) [1] 0.83 0.85 0.87 0.89 0.90 0.92 0.93 > pt(c(1.0,1.1,1.2,1.3,1.4,1.5,1.6),10) [1] 0.83 0.85 0.87 0.89 0.90 0.92 0.93 1. A mixture of pulverized fuel ash and Portland ce- ment should have a compressive strength of more than 1000KN/m 3 . The mixture will not be used unless experimental evidence indicates that the strength specification has been met. Suppose com- pressive strength for specimens of this mixture is normally distributed with σ 2 = 98 2 . The sample mean of compressive strength for 10 specimens is ¯ x = 1050 . (1) What are the appropriate null and alternate hy- pothesis (5 points)? (2) What would be the appropriate test statistic for the hypothesis testing? What is the probability dis- tribution of your test statistic when H 0 is true? (5 points each) (3) Do hypothesis testing at 85% level. Has the strength specification been met (10 points)?
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