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=300, x=140, critical value for 90% CL=1.645

Answer 1

Solution :

Given that,

n = 300

x = 140

Point estimate = sample proportion = = x / n = 140 / 300 = 0.467

1 - = 1 - 0.467 = 0.533

At 90% confidence level

= 1 - 90%

=1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645}

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

= 1.645 (((0.467 * 0.533) / 300)

= 0.0474