SOLUTION: In a survey of 2383 U.S. adults, 1073 think that there should be more government regulation of oil companies. (a) Construct a 95% confidence interval for the population proportio

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Question 1139079: In a survey of 2383 U.S. adults, 1073 think that there should be more government
regulation of oil companies.
(a) Construct a 95% confidence interval for the population proportion p of U.S.
adults who think that there should be more government regulation of oil
companies. (Be sure to verify that the assumptions are met for the procedure
you use.)
(b) Find the minimum sample size needed to estimate p that ensures with 99%
confidence that the estimate is accurate within 3% (E = 0.03) of the population
proportion. Use p hat = q hat = 0.5 in your calculation.

I have been working on this problem all day and I do not know what to do.

Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
assume random sample, and numbers and probability are sufficiently large to use normal approximation.
The point estimate is 1073/2383=0.450
the half-interval is z*sqrt(p*1-p)/n)=1.96*sqrt(0.45*0.55/2383)
0.45+/-1.96(1.01), the half-interval is 0.02
the whole interval is (0.43, 0.47)

The half-interval is z0.995*sqrt (p*(1-p)/n)
z is 2.576
p and 1-p are 0.5
the half-interval equals the error of 0.03
square both sides and z^2*p(1-p)/n=0.0009
so 6.64*0.25=0.0009n
n=1844.44 or 1845