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)`

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}=(760)/(1000)=0.76`

Critical value for 95% confidence interval =
`z_(\alpha/2)=1.96`

Confidence interval :

`\hat{p}\pm z_(\alpha/2)\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\\\=0.76\pm(1.96)\sqrt{(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)`