Question

A researcher for the U.S. Department of the Treasury wishes to estimate the percentage of Americans who support abolishing the penny. What size sample is necessary to estimate the proportion with 95% confidence of being within 3% of the true proportion.

i. The value for z α / 2to use in the formula is                            [ Select ]                       ["2.33", "1.645", "2.575", "1.96", "0.95"]         .

ii. The value for E to use in the formula is                            [ Select ]                       ["0.03", "0.5", "0.95", "3"]         .

iii. Using the answers to parts (i) and (ii), the correct sample size is                            [ Select ]                       ["4268.4", "4269", "1068", "1067.11", "0.1067", "1067", "4268"]         .

Answer 1

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 3% = 0.03

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )

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

= (1.96 / 0.03)2 * 0.5 * 0.5

= 1067.11

Sample size =1068