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 750 likely voters was taken. Four hundred fifty of those sampled favored the school bond initiative. The 95% confidence interval for the true proportion of voters favoring the initiative is _____

Answer 1

Answer: (0.565, 0.635)

Explanation:

Given : Sample size : n= 750

The number of voters favored the school bond initiative =450

Then , the proportion of voters favored the school bond initiative :

`p=(450)/(750)=0.6`

Significance level :
`1-0.95=0.05`

Critical value :
`z_(\alpha/2)=1.96`

The confidence interval for population proportion is given by :-

`p\ \pm\ z_(\alpha/2)\sqrt{(p(1-p))/(n)}\\\\=0.6\pm (1.96)\sqrt{((0.6)(0.4))/(750)\approx0.6\pm0.035\\\\=(0.6-0.035,0.6+0.035)\\\\=(0.565, 0.635)`

Hence, the 95% confidence interval for the true proportion of voters favoring the initiative is (0.565, 0.635).