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.

(a) A poll taken in July 2010 estimates this proportion to be 0.3 Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.02?

A sample of adults is needed to obtain a 99.5% confidence interval with a margin of error of 0.02 .

B. Estimate the sample size needed if no estimate of p is available.

Answer 1

Solution:

a ) Given that,

= 0.3

1 - = 1 - 0.3 = 0.7

margin of error = E = 0.02

At 99.5% confidence level the z is ,

  = 1 - 99.5% = 1 - 0.995 = 0.005

/ 2 = 0.005 / 2 = 0.0025

Z/2 = Z0.0025 = 2.807

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

= (2.807/ 0.02)2 * 0.3 * 0.7

= 4137

n = sample size = 4137

b ) Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 0.02

At 99.5% confidence level the z is ,

  = 1 - 99.5% = 1 - 0.995 = 0.005

/ 2 = 0.005 / 2 = 0.0025

Z/2 = Z0.0025 = 2.807

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

= (2.807/ 0.02)2 * 0.5 * 0.5

= 4925

n = sample size = 4925