SOLUTION: Use the given data to find the minimum sample size required to estimate the population proportion. Margin of error: 0.04; confidence level: 90%; from a prior study, the best point

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Question 863476: Use the given data to find the minimum sample size required to estimate the population proportion. Margin of error: 0.04; confidence level: 90%; from a prior study, the best point estimate is 0.17.
A. 212
B. 717
C. 198
D. 298
E. 239
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The margin of error (ME) for a proportion is


ME+=+z%2A+sqrt%28+%28p%2A%281-p%29%29%2Fn%29


where...


ME = margin of error

z = critical z value (use a table or a calculator to compute this value)

p = proportion

n = sample size

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In this case, we know...


ME = 0.04, this is given when they say "Margin of error: 0.04"

z = 1.645 and you can use this table to help find it. Look in the row that starts with infinity. This row is towards the very bottom. In this row, look for the number that is above the 90% confidence level

p = 0.17 (given) "he best point estimate is 0.17"

n = unknown

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To sum things up, we know

ME = 0.04
z = 1.64 (again, you use this table)
p = 0.17
n = unknown

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Now take what we know and plug it into the given formula at the top of the page. Then solve for n. We will round up to the nearest whole number (since you can't have a fraction of a person or object in the sample). We will round up to make sure the ME is 0.04 or less. If we round down, then the ME could be too big.


ME+=+z%2A+sqrt%28+%28p%2A%281-p%29%29%2Fn%29


0.04+=+1.645%2A+sqrt%28+%280.17%2A%281-0.17%29%29%2Fn%29


0.04%2F1.645+=+sqrt%28+%280.17%2A%281-0.17%29%29%2Fn%29


0.0243161094225+=+sqrt%28+%280.17%2A%281-0.17%29%29%2Fn%29


%280.0243161094225%29%5E2+=+%280.17%2A%281-0.17%29%29%2Fn


0.00059127317744+=+%280.17%2A%281-0.17%29%29%2Fn


0.00059127317744+=+%280.17%2A0.83%29%2Fn


0.00059127317744+=+0.1411%2Fn


0.00059127317744n+=+0.1411


n+=+0.1411%2F0.00059127317744


n+=+238.637579690173


n+=+239 Round UP to the nearest whole number. We round UP to make sure we clear the hurdle (and make sure the Margin of Error (ME) is 0.04 or less)


So the minimum sample size needed is 239.


The answer is Choice E) 239.