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How large of sample is needed in order to have a margin of error of 3%...

How large of sample is needed in order to have a margin of error of 3% when n = 290, x = 121, and LaTeX: \alpha = 0.01

Math   Statistics-And-Probability   
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Answer #1

Solution,

Given that,

= 121 / 290 = 0.417

1 - = 1 - 0.417 = 0.583

margin of error = E = 0.03

= 0.01

/2 = 0.005

Z/2 = Z0.005  = 2.576

sample size = n = (Z / 2 / E )2 * * (1 - )

= (2.576 / 0.03 )2 * 0.417 * 0.583

= 1792.47

sample size = n = 1793

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