Question

Local government officials are interested in knowing if taxpayers are willing to support a school bond initiative that will require an increase in property taxes. A random sample of 1,200 likely voters was taken. Six hundred fifty of those sampled favored the school bond initiative. The 95% confidence interval for the true proportion of voters favoring the initiative is ________.

Group of answer choices

[0.565, 0.635]

[0.500, 0.700]

[0.513, 0.570]

[0.541, 0.639]

Answer 1

Givevn : n=1200 , X=650

The sample proportion is , p=X/n=650/1200=0.5417

q=1-p=1-0.5417=0.4583

Now , $Z_{\alpha/2}=Z_{0.05/2}=1.96$ ; From standard normal distribution table

Therefore , the 95% confidence interval for the true proportion of voters favoring the initiative is ,

$p\pm Z_{\alpha/2}\sqrt{\frac{pq}{n}}$

$0.5417\pm 1.96*\sqrt{\frac{0.5417*0.4583}{1200}}$

$0.5417\pm 0.0282$