How\'s the economy? A pollster wants to construct a 99% confidence interval (or
ID: 3155953 • Letter: H
Question
How's the economy? A pollster wants to construct a 99% confidence interval (or the proportion of adults who believe that economic conditions are getting better. A poll taken in July 2010 estimates this proportion to be 0.43. Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.05? A sample of 6S1 adults is needed to obtain a 90% confidence interval with a margin of error of 0.05. Estimate the sample size needed if no estimate of p is available. A sample of adults is needed to obtain a 99% confidence interval with a margin of 0.05%.Explanation / Answer
1.
Note that
n = z(alpha/2)^2 p (1 - p) / E^2
where
alpha/2 = 0.005
Using a table/technology,
z(alpha/2) = 2.575829304
Also,
E = 0.05
p = 0.43
Thus,
n = 650.4852628
Rounding up,
n = 651 [ANSWER]
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2.
Note that
n = z(alpha/2)^2 p (1 - p) / E^2
where
alpha/2 = 0.005
As there is no previous estimate for p, we set p = 0.5.
Using a table/technology,
z(alpha/2) = 2.575829304
Also,
E = 0.05
p = 0.5
Thus,
n = 663.4896601
Rounding up,
n = 664 [ANSWER]
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