Question

The American Heart Association is about to conduct an anti-smoking campaign and wants to know the fraction of Americans over 21 who smoke. In an earlier study, the population proportion was estimated to be 0.3 . How large a sample would be required in order to estimate the fraction of Americans over 21 who smoke at the 80% confidence level with an error of at most 0.03? Round your answer up to the next integer.

Answer 1

Solution :

Given that,

= 0.3

1 - = 0.7

At 80% confidence level the z is ,

= 1 - 80% = 1 - 0.80 = 0.20

/ 2 = 0.20 / 2 = 0.10

Z_/2 = Z _0.10 = 1.28

margin of error = E = 0.03

Z_/2 = 1.28

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

= (1.28 / 0.03)² * 0.3 * 0.7

= 383

sample size = n = 383