Unformatted text preview: 1200 people in North Carolina, and found that 684 were supporting the candidate. We would like to construct a 95% conFdence interval for θ , the proportion of people who support the candidate. As we saw in lecture, using the central limit theorem, an (approximate) 95% conFdence interval can be deFned as ˆ Θ= ˆ Θ n1 . 96 r v n , ˆ Θ + = ˆ Θ n + 1 . 96 r v n where v = Var( X i ), and ˆ Θ n = ( X 1 + . . . + X n ) /n . Unfortunately, we don’t know the value for v . Construct conFdence intervals for θ using the following three ways of estimating or bounding the value for v (in each case simply assume that v is equal to the given estimate; note that this is a further approximation in cases (a) and (b)). (a) ˆ S 2 n = 1 n1 n s i =1 ( X iˆ Θ n ) 2 (b) ˆ Θ n (1ˆ Θ n ) (c) The most conservative upper bound for the variance. Page 1 of 1...
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 Spring '11
 Proasin
 Computer Science, Electrical Engineering, Central Limit Theorem, Probability theory, Probabilistic Systems Analysis, sample voter responses, conservative upper bound

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