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A city planner wishes to determine the proportion of residents who own their home. He wishes to be 95% confident that the estimate is within 2 percentage points of the true percentage. (a) How large should the sample size be? A previous estimate indicated that 40% of the residents own their home (b) How large should the sample size be if no previous estimate is available.

so far i got 1-alpha=.95
where i got alpha to be .05
alpha/2 = .025 so Z.025=1.96

1.96sqrt(pq/n)=.02

thats where I'm having difficulty because i'm not sure im approaching this the correct way

sandy
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    $\hat{p}=.4$ and $\hat{q}=.6$, if there is no previous estimate then we have $\hat{p} = .5$ and $\hat{q} = .5$. The reason we assume $\hat{p}=\hat{q} = .5$ when we have no estimate is because this yields the highest possible $\hat{p}\cdot\hat{q}$ which is in a sense the worst case scenario requiring the largest $n$ to be $95%$ confident. – EgoKilla May 12 '14 at 03:32

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