tut_9_Chap_9_sol - CollegeofEngineering,QatarUniversity

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College of Engineering, Qatar University Page 1 of 8 Probability and Statistics, GENG200 2B Tutorial - 9 Question Sections 9-1 Page 303: 1) 9-3 2) 9-4 3) 9-5 Answer: 9-3 a) nm H nm H 20 : , 20 : 1 0 < = σ b) This result does not provide strong evidence that the standard deviation has not been reduced. This result says that we do not have enough evidence to reject the null hypothesis . It is not support for the null hypothesis. 9-4 a) Newtons H Newtons H 25 : , 25 : 1 0 < = μ b) No, this results only means that we do not have enough evidence to support H 1 9-5 a) α = P(reject H 0 when H 0 is true) = P( X 11.5 when μ = 12) = 4 / 5 . 0 12 5 . 11 / n X P = P(Z 2) = 0.02275. The probability of rejecting the null hypothesis when it is true is 0.02275. b) β = P(accept H 0 when μ = 11.25) = ( ) 25 . 11 5 . 11 = > when X P = > 4 / 5 . 0 25 . 11 5 . 11 / n X P = P(Z > 1.0) = 1 P(Z 1.0) = 1 0.84134 = 0.15866 The probability of accepting the null hypothesis when it is false is 0.15866. c) β = P(accept H 0 when μ = 11.25) = = () 5 . 11 5 . 11 = > when X P = > 4 / 5 . 0 5 . 11 5 . 11 / n X P = P(Z > 0) = 1 P(Z 0) = 1 0.5 = 0.5 The probability of accepting the null hypothesis when it is false is 0.5
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College of Engineering, Qatar University Page 2 of 8 9-7 The critical value for the one-sided test is n z X / 5 . 0 12 α a) α =0.01, n=4, from Table III -2.33 = z α and X 11.42 b) α =0.05, n=4, from Table III -1.65 = z α and X 11.59 c) α =0.01, n=16, from Table III -2.33 = z α and X 11.71 d) α =0.05, n=16, from Table III -1.65 = z α and X 11.95 9-8 a) β = P( X >11.59|μ=11.5)=P(Z>0.36)=1-0.6406=0.3594 b) β = P( X >11.79|μ=11.5)=P(Z>2.32)=1-0.9898=0.0102 c) Notice that the value of β decreases as n increases
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College of Engineering, Qatar University Page 3 of 8 Quiestion: Section 9-1, Page 303 4) 9-10 Answer: 9-10 a) α = P( X 98.5) + P( X > 101.5) =
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This note was uploaded on 10/12/2011 for the course STATISTICS 101 taught by Professor Nazim during the Spring '10 term at Qatar University.

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tut_9_Chap_9_sol - CollegeofEngineering,QatarUniversity

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