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Homeowrk 6 Solution - H W6 Solution 6.30 = 1 = 1.5 =.05...

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HW6 Solution 6.30 1; 1.5; .05 μ σ α = = = Margin of Error (E) = 1 1 4 =.25 2 2 2 2 /2 2 2 ( ) 1.96 (1.5) .25 138.29 139 z n E α σ = = = 6.40 (a) /2 .025 69 ˆ .204 339 .05 ˆˆ(1 ) ˆ 95% . . (.204)(.796) .204 339 (.204)(.796) .204 1.96 339 .204 (1.96) (.022) .204 .043 (.161, .247) x p n p p p z n Wald C I z α α = = = = - ± = ± = ± = ± = ± = (c-1) We are 95% confident that the probability of an adverse reaction to the vaccine is between .161 and .247. (b) 2 2 /2 .025 2 2 /2 .025 2 2 .5( ) 69 .5( ) ( ) 339 ( ) 69 .5(1.96) 70.92 .207 339 (1.96) 342.84 .05 x z z p n z z α α α + + = = + + + = = = + = % /2 2 /2 .025 2 /2 2 (1 ) ( ) 95% . . (.207)(.793) .207 339 ( ) (.207)(.793) .207 1.96 339 1.96 .207 (1.96) (.022) .207 .043 (.164, .250) p p p z n z Wilson C I z z α α α - ± + = ± + = ± + = ± = ± = % % % (c-2) We are 95% confident that the probability of an adverse reaction to the vaccine is between .164 and .250. 6.48 (a) /2 .025 103 ˆ .072 1438 .05 ˆˆ(1 ) ˆ 95% . . (.072)(.928) .072 1438 (.072)(.928) .072 1.96 1438 .072 .013 (.059, .085) x p n p p p z n Wald C I z α α = = = = - ± = ± = ± = ± = We are 95% confident that the probability of contracting an STD within six months after being part of a counseling program
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