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.

Part: 0 / 20 of 2 Parts Complete
Part 1 of 2
(a) A poll taken in July 2010 estimates this proportion to be 0.37. Using this estimate,
what sample size is needed so that the confidence interval will have a margin of error of 0.03?

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,

= 0.37

1 - = 1-0.37 = 0.63

margin of error = E = 0.03

At 99.5% confidence level

= 1-0.99.5% =1-0.995 =0.005

/2 =0.005/ 2= 0.0025

Z/2 = Z0.0025 = 2.807

Z/2 = 2.807

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

= (2.807/0.03)2 *0.37*0.63

= 2041

sample size = n = 2041

A sample of 2041 adults is needed to obtain a 99.5 confidence interval with a margin of error of 0.03.