SOLUTION: A report states that 40% of home owners had a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within 3%

Question 1086255: A report states that 40% of home owners had a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within 3% with 99% confidence?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
interval is 0.03
2.576*SE is 99% confidence
SE is sqrt (0.4)(0.6) or p(1-p)/n
Therefore,
0.03=2.576* sqrt (0.24/n)
square both sides
0.0009=6.64*0.24/n
0.0009n=1.59. I haven't rounded, but dividing now by 0.0009 gives n=1769.54, or 1770.
RELATED QUESTIONS
A report states that 40% of home owners had a vegetable garden. How large a sample is... (answered by stanbon)

A report states that 54% of home owners had a vegetable garden. How large a sample is... (answered by stanbon)

A report states that 44% of home owners have a vegetable garden. How large a sample is... (answered by stanbon)

A report states that 46% of car owners had a V8 engine. How large a sample is needed to... (answered by stanbon)

A federal report indicated that 27% of children ages 2 to 5 years had a good diet—an... (answered by Theo)

A federal report stated that 88% of children under age 18 were covered by health... (answered by stanbon)

A survey of 36 "iPhone" owners showed that the purchase price has a sample mean of $450... (answered by stanbon)

(a) In a random sample of 150 persons having their lunch at the University cafeteria on... (answered by stanbon)

An advertising firm states that 27% of households will buy something on the Internet next (answered by robertb)