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.

90% confidence; n = 311, x = 140

Answer 1

Solution :

Given that,

n = 311

x = 140

= x / n =140 /311 = 0.450

1 - = 1 - 0.450 = 0.550

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

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

= 1.645 * (((0.450 * 0.550) / 311) = 0.046

margin of error of E = 0.046