Question

We are given an estimated population proportion of a specific event is p = 0.41. What would be the required sample size needed to be within a margin of error (bound on the error of estimation) of 0.023 with a 90% confidence level? Round UP to the nearest integer.

A. 860

B. 1757

C. 1238

D. 1781

E. 1279

Answer 1

Solution,

Given that,

= 0.41

1 - = 1 - 0.41 = 0.59

margin of error = E = 0.023

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645

sample size = n = (Z / 2 / E )2 * * (1 - )

= (1.645 / 0.023 )2 * 0.41 * 0.59

= 1237.41

sample size = n = 1238

Correct option is C