Question

Suppose it’s 1974, and you’re working as a pollster. You want to figure out how many people you’d have to survey to get a 97.5% confidence interval of ±4% for the proportion of Americans who say baseball is their favorite sport.

(a) Find an appropriate sample size assuming you have no previous information.

(b) Now suppose that your helpful intern has found a Gallup poll from 1972 in which 19% of Americans surveyed said that baseball was their favorite sport.4 Use this information to find an appropriate sample size.

Answer 1

Solution,

Given that,

a) =  1 - = 0.5

margin of error = E = 0.04

At 97.5% confidence level

= 1 - 97.5%  

= 1 - 0.975 =0.025

/2 = 0.0125

Z/2 = Z0.0125  = 2.241

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

= (2.241 / 0.04)2 * 0.5 * 0.5

= 784.70

sample size = n = 785

b) = 0.19

1 - = 1 - 0.19 = 0.81

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

= (2.241 / 0.04)2 * 0.19 * 0.81

= 483.06

sample size = n = 484