Question

In a sample of 430 residents of Georgetown County, 165 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 the p(proportion) value to 2 decimal places and final 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?

(Click to select)  Yes  No

Answer 1

$\hat{p} =165/430 = 0.3837$

For 95% confidence level , $z_{c}=1.96$

95% confidence interval for true proportion

$\hat{p}\pm z_{c}*\sqrt{\hat{p}(1-\hat{p})/n}$

= 0.3837 $\pm$ 0.04596

= (0.338, 0.430)

No, it is not reasonable to conclude that majority of tax payers feel that taxes are too high.

As upper limit of confidence interval is less than 0.5 or 50% . So we can say that less than 50% feel that taxes are too high.