Question

In a sample of 200 residents of Georgetown County, 120 reported they believed the county real estate taxes were too high. Develop a 95 percent confidence interval for the proportion of residents who believe the tax rate is too high. (Round your answers to 3 decimal places.) Confidence interval for the proportion of residents is up to . Would it be reasonable to conclude that the majority of the taxpayers feel that the taxes are too high?

Answer 1

(a) The confidence interval is 0.5321<π<0.6679

(b) It can be said, with more than 95% certainty, that the majority of the taxpayers feel that the taxes are too high.

Explanation:

First, we calculate the proportion p

`p=120/200=0.6`

For a 95% confidence interval, z-score is 1.96.

The lower and upper limit of the confidence interval can be calculated as

`LL = p-z*\sigma_(p)=p-z*\sqrt{(p(1-p))/(N) } \\LL=0.6-1.96*\sqrt{(0.6*0.4)/(200) }=0.6 - 1.96*0.0346=0.6-0.0679=0.5321\\\\UL=p+z*\sigma_(p)=p+z*\sqrt{(p(1-p))/(N) } \\UL=0.6+0.0679=0.6679`

The confidence interval is 0.5321<π<0.6679

(b) The lower limit is above 53%, so it can be concluded that the majority of the taxpayers feel that the taxes are too high.