According to a survey of 673 small business participants in

According to a survey of 673 small business participants in the Constant Contact Small Biz Council in May of 2013, 384 of the respondents say it is harder to run a small business now than it was 5 years ago. When estimating the population proportion, what is the 95% confidence interval estimating the proportion of businesses who believe it is harder to run a business now than 5 years ago?

A. (-0.53318 , 0.60798)

B. (0.5515 , 0.58966)

C. (0.54919 , 0.59196)

D. (0.39202 , 0.46682)

E. (0.53318 , 0.60798)

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)=384
Sample Size(n)=673
Sample proportion = x/n =0.5706
Confidence Interval = [ 0.5706 ±Z a/2 ( Sqrt ( 0.5706*0.4294) /673)]
= [ 0.5706 - 1.96* Sqrt(0.0004) , 0.5706 + 1.96* Sqrt(0.0004) ]
= [ 0.53318,0.60798]