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 = 305, x = 146

Answer 1

Solution :

Given that,

n = 305

x = 146

Point estimate = sample proportion = = x / n = 146 / 305 = 0.479

1 - = 1- 0.479 = 0.521

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 (((0.479 * 0.521 ) / 305 )

= 0.0471

Margin of error = 0.0471