Assume that a sample is used to estimate a population
proportion p. Find the margin of error E that corresponds to the
given statistics and confidence level. Round the margin of error to
four decimal places.
95% confidence; n = 334, x = 44
solution :
Given that,
n = 334
x = 44
= x / n = 44/ 334 = 0.132
1 - = 1 - 0.132 = 0.868
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
Margin of error = E = Z / 2 * (( * (1 - )) / n)
= 1.96 * (((0.132 * 0.868) / 334) = 0.0363
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