Question

​it's believed that as many as 2222​% of adults over 50 never graduated from high school. we wish to see if this percentage is the same among the 25 to 30 age group. ​a) how many of this younger age group must we survey in order to estimate the proportion of​ non-grads to within 44​% with​ 90% confidence?

Answer 1

The given values are:

p =  22% = 0.22

Zc = 1.645 at 90% confidence level.

margin of error, E = 0.04

 

The formula we can use here is:

E = sqrt(pq/n) * Zc

 0.04 = sqrt(0.22*(1-0.22)/n)*1.645

n = (0.22*(1-0.22))*(1.645/0.04)^2

n = 290.22

 

hence minimum sample size = 290