Answer
n=300,p̂ = 0.43 = ,q = 1-p̂ = 0.57
when confidence interval = 95%
α= 1-0.95 = 0.05.
α/2 = 0.025
1-0.025 = 0.975
From the table,
$z_α/_2$ = 1.96
p̂ - $z_α/_2$ $\sqrt \frac{p̂q̂}{n}$ < p < p̂ + $z_α/_2$ $\sqrt \frac{p̂q̂}{n}$
= 0.43 - 1.96$\sqrt \frac{0.43*0.57}{300}$ < p < 0.43 + 1.96$\sqrt \frac{0.43*0.57}{300}$
= 0.374 < p < 0.486
= 37.4% < p < 48.6%
Hence, we can say that the true proportion of Republican voters who feel this way with 95% confidence level is between 37.4% and 48.6%.
