At issue is the proportion of people in a particular county

At issue is the proportion of people in a particular county who do not have health care insurance coverage. A simple random sample of 240 people was asked if they have insurance coverage, and 66 replied that they did not have coverage. Based on these sample data, determine the 95% confidence interval estimate for the population proportion. (0.239, 0.321) (0.224, 0.336) (0.259, 0.301) (0.268, 0.292)

Solution

CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=66
Sample Size(n)=240
Sample proportion = x/n =0.275
Confidence Interval = [ 0.275 ±Z a/2 ( Sqrt ( 0.275*0.725) /240)]
= [ 0.275 - 1.96* Sqrt(0.0008) , 0.275 + 1.96* Sqrt(0.0008) ]
= [ 0.2185,0.3315]