Answer
$n=n_1=n_2=1406$
Work Step by Step
$level~of~confidence=(1-α).100$%
$95$% $=(1-α).100$%
$0.95=1-α$
$α=0.05$
$z_{\frac{α}{2}}=z_{0.025}$
If the area of the standard normal curve to the right of $z_{0.025}$ is 0.025, then the area of the standard normal curve to the left of $z_{0.025}$ is $1−0.025=0.975$
According to Table V, the z-score which gives the closest value to 0.975 is 1.96.
Now, the sample size:
$E=0.03$ (within 3 percentage points)
$p̂ _1=0.219$
$p̂ _2=0.197$
$z_{\frac{α}{2}}=1.96$
$n=n_1=n_2=[p̂_1(1-p̂_1)+p̂_2(1-p̂_2)](\frac{z_{\frac{α}{2}}}{E})^2$
$n=n_1=n_2=[0.219(1-0.219)+0.197(1-0.197)](\frac{1.96}{0.03})^2$
$n=n_1=n_2=1405.3$
Round up:
$n=n_1=n_2=1406$
