Question

​It's believed that as many as 21​% 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 6​% with​ 90% confidence?

Answer 1

Solution :

Given that,

= 0.21

1 - = 1 - 0.21 = 0.79

margin of error = E = 6% = 0.06

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z _0.05 = 1.645

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

= (1.645 / 0.06)² * 0.21 * 0.79

= 124.7 = 125

sample size = 125

125 of this younger age group must we survey .