Question

Consider eligible voters between the ages of 18-30, and those older than 30. A 95% confidence interval has width 0.01 for P_youngerthan30 - P_olderthan30 and independent samples are taken of size n of each population. How large of an N do we need?

Answer 1

Solution:

1) Z: Divide the confidence interval by two and using the z-table let us find the z-score.

So, 0.95/2=0.475

The z-score for 0.475 is1.96

2)Margin of error(E): Divide the given width by 2.

So, 0.01/2=0.005

3) : Since percentage is not given, let us use 50%

4) =1-=1-0.5=0.5

5) Formula to calculate sample size is n= (Z /E)2**

= (1.96/0.005)2*0.5*0.5

=38416