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How large a sample is needed to estimate the true proportion of children with good diets within 2% with 95%?

A federal report indicated that 27% of children ages 2 to 5 years had a good diet—an increase previous years. How large a sample is needed to estimate the true proportion of children with good diets within 2% with 95% confidence?

sample size n is (t/b)^2 s^2, where t is critical value for conf. level (here 1.96), b is margin of error
(here .02), and s^2 is variance in population (here p(1-p)=.27(.73)=.1971).

So n=(1.96/.02)^2 (.1971) = 1892.9, and round up to 1,893

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1. May 19th, 2012 at 10:08 | #1

sample size n is (t/b)^2 s^2, where t is critical value for conf. level (here 1.96), b is margin of error
(here .02), and s^2 is variance in population (here p(1-p)=.27(.73)=.1971).

So n=(1.96/.02)^2 (.1971) = 1892.9, and round up to 1,893
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