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Assignment+4-sol

# Assignment+4-sol - Assignment 4 Problem 1 a The sample...

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Assignment 4 Problem 1. a) The sample proportion of people suffered from heart disease for the the smoker group is 3393 . 0 56 19 ˆ 1 = = p . The sample proportion of people suffered from heart disease for the the non-smoker group is 1736 . 0 144 25 ˆ 2 = = p . b) Let p 1 and p 2 be the proportions of people suffered from heart disease for the smokers and non-smokers respectively. 0 : 2 1 = - p p H a vs 0 : 2 1 - p p H a Test Statistic + - - = 2 1 2 1 1 1 ) ˆ 1 ( ˆ ˆ ˆ n n p p p p Z where 22 . 0 200 44 ˆ = = p 05 . 0 645 . 1 5396 . 2 144 1 56 1 ) 22 . 0 1 ( 22 . 0 1736 . 0 3393 . 0 z = = + - - = H 0 is rejected at 5% level of significant. There is sufficient evidence that smokers have a higher incidence of heart disease than nonsmokers. c) p-value = Pr(Z>2.5396) =0.5 0.4945 = 0.0055 d) 1 . 0 : 2 1 = - p p H a vs 1 . 0 : 2 1 - p p H a Test Statistic ( 29 ( 29 645 . 1 9288 . 0 144 ) 1736 . 0 1 ( 1736 . 0 56 ) 3393 . 0 1 ( 3393 . 0 1 . 0 1736 . 0 3393 . 0 ) ˆ 1 ( ˆ ) ˆ 1 ( ˆ 1 . 0 ˆ ˆ 2 2 2 1 1 1 2 1 / = - + - - - = - + - - - = n p p n p p p p Z H 0 is not rejected at 5% level of significant. This is not sufficient evidence to say the

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