Question

Multiple choice, please help ASAP

suppose a study estimated that 78% of the residents of a town (with an error range of ±8 percentage points at 95% confidence) favor expanding the park and recreation department. which of the following percentages of the town's residents may favor expanding the park and recreation department?


A. 62%


B. 52%


C. 92%


D. 72%

Answer 1

Answer: 72% - Apex

Explanation:

Answer 2

Answer: D. 72%

Explanation:

The confidence interval for proportion is given by :-

`p\ \pm E`, where E is the margin of error.

Given : Sample size :
`n=1000`

The proportion of the residents of a town : p=0.78

Margin of error :
`E=0.08`

Significance level :
`1-0.95=0.05`

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

Now, the 95% confidence Interval for the proportion of residents of a town will be :-

`0.78\ \pm 0.08=(0.7,\ 0.86)`

Thus , the

95% confidence Interval for the percentage of residents of a town will be (70%, 86%)

From all the given options only 72 % lies in the confidence interval.

Hence, 72% of the town's residents may favor expanding the park and recreation department