Question

The results of a survey conducted by the Sierra Club in the spring of 1999 indicates that voters in the United States supported the idea of more public money being spent on conservation (Haya El Nasser, “Conservation has clout in Congress,” USA Today, May 11, 1999, p.13A). In a survey of 861 registered voters, half the people indicated that they would rather spend $2 billion of the federal government’s budget surplus to protect wildlands than on national defense. Suppose that you wished to conduct a follow-up survey to estimate the proportion of U.S. voters who currently favour such a proposal. Determine the sample size needed to estimate this population proportion to within +/- 0.02 with 95% confidence.

Answer 1

Solution,

Given that,

=  1 - = 0.5

margin of error = E = 0.02

At 95% confidence level

= 1 - 95%

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025  = 1.96

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

= (1.96 / 0.02 )2 * 0.5 * 0.5

= 2401

sample size = n = 2401