Question

A researcher wishes to​ estimate, with 95​% ​confidence, the population proportion of adults who think the president of their country can control the price of gasoline. Her estimate must be accurate within 2​% of the true proportion. ​a) No preliminary estimate is available. Find the minimum sample size needed. ​b) Find the minimum sample size​ needed, using a prior study that found that 34​% of the respondents said they think their president can control the price of gasoline.

Answer 1

Solution :

Given that,

margin of error = E = 0.02

Z_/2 = 1.96

(a)

= 0.5

1 - = 0.5

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

= (1.96 / 0.02)² * 0.5 * 0.5

= 2401

sample size = n = 2401

(b)

= 0.34

1 - = 0.66

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

= (1.96 / 0.02)² * 0.34 * 0.66

= 2401

sample size = n = 2156