Question

A pollster wishes to estimate the true proportion of U.S. voters who oppose capital punishment. How...

A pollster wishes to estimate the true proportion of U.S. voters who oppose capital punishment. How many voters should be surveyed in order to be 95% confident that the true proportion is estimated to be within 5%? (Round answer to the nearest whole number.)

Math   Statistics-And-Probability   
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Answer #1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

Margin of error = E = 5% = 0.05

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

Sample size = (  Z/2 / E)2 * * (1 - )

= (1.96 / 0.05)2 * 0.5 * 0.5

= 384.16 = 384

Sample size = n = 384

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