Question

How's the economy? A pollster wants to construct a 99.5% confidence interval for the proportion of
adults who believe that economic conditions are getting better.

b) Estimate the sample size needed if no estimate of P is available.

A sample of _ adults is needed to obtain a 99.5 confidence interval with a margin of error of 0.03.

Answer 1

Solution,

Given that,

=  1 - = 0.5

margin of error = E = 0.03

At 99.5% confidence level

= 1 - 99.5%

= 1 - 0.99.5 =0.005

/2 = 0.0025

Z/2 = Z0.0025  = 2.807

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

= (2.807 / 0.03 )2 * 0.5 * 0.5

= 2188.68

sample size = n = 2189