Question

A random sample of 1000 registered voters in Flagstaff found 760 registered voters who support immigration reform. Find a 95% confidence interval for the true percent of registered voters in Flagstaff who support immigration reform.

Answer 1

Answer: $(0.7335,\ 0.7865)$

Step-by-step explanation:

Given : A random sample of 1000 registered voters in Flagstaff found 760 registered voters who support immigration reform.

sample size : n= 1000

sample proportion: $\hat{p}=\dfrac{760}{1000}=0.76$

Critical value for 95% confidence interval = $z_{\alpha/2}=1.96$

Confidence interval :

$\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\=0.76\pm(1.96)\sqrt{\dfrac{0.76(1-0.76)}{1000}}\\\\=0.76\pm0.0264708866493\\\\\approx0.76\pm0.0265\\\\=(0.76-0.0265,\ 0.76+0.0265)=(0.7335,\ 0.7865)$

Hence, the  95% confidence interval for the true percent of registered voters in Flagstaff who support immigration reform: $(0.7335,\ 0.7865)$