Question

A researcher examined a random sample of 300 homes in a small city and found that 52 had solar panels installed on their roofs. Use the sample to construct a 99% confidence interval for the proportion of all homes in the city that have solar panels installed on their roofs.

What is the 99% confidence interval?

Answer 1

We have given here,                          
                          
x=52                      
n=300                      
Estimate for sample proportion                          
$\hat{p}=\frac{x}{n}=\frac{ 52 }{ 300 }= 0.1733$
Level of significance is =1-0.99=0.01                  
Z critical value(using Z table)=2.576                  

$\hat{p}\pm Z*\sqrt{\frac{\hat{p}*(1-\hat{p})}{n}}= 0.1733 \pm 2.576 \sqrt{\frac{\ 0.1733 * 0.8267 }{ 300 }}=( 0.117 , 0.2296 )$