Question

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 = 356, x = 49

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 49 / 356 = 0.1376

1 - = 1 - 0.1376 = 0.8624

Z/2 = Z_0.025 = 1.96

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.96 (((0.1376 * 0.8624) / 356 )

= 0.0358

A 95% confidence interval for population proportion p is ,

± E

= 0.1376 ± 0.0358

= ( 0.1018, 0.1734 )