Question 1110326: A researcher wishes to estimate, with
9999%
confidence, the population proportion of adults who think the president of their country can control the price of gasoline. Her estimate must be accurate within
44%
of the true proportion.
a) No preliminary estimate is available. Find the minimum sample size needed.
b) Find the minimum sample size needed, using a prior study that found that
1818%
of the respondents said they think their president can control the price of gasoline.
c) Compare the results from parts (a) and (b).
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Within 4% and confidence 99%
the error 0.04=z* sqrt (SE), where z=2.576 and SE is sqrt (p*(1-p))/n. Use 0.5 when no estimate is available, since that is the most conservative (largest) product of two decimals whose sum is 1.
2.576*sqrt(0.25)/sqrt (n) equals error
2.576*0.5/sqrt (n)=0.04
1.288/0.04=sqrt(n); square both sides
n=1036.84 or 1037.
With a known fraction of 0.18, p*(1-p)=0.1476
(1.288/0.1476)^2=76.15 or 77
When a prior estimate is available and is significantly different from 0.5, the sample size falls dramatically.
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