Given that a
researcher takes a simple random sample of 71 homes in the city and
finds that the mean square footage is 1468 with a standard deviation of
213 square feet.
The 90% confidence interval for the mean square footage of all homes in that city is given by
[tex]90\%\ C.1.=\bar{x}\pm1.65\left( \frac{\sigma}{\sqrt{n}} \right) \\ \\ =1468\pm1.65\left( \frac{213}{\sqrt{71}} \right)=1468\pm1.65(25.28) \\ \\ =(1468-41.7,\ 1468+41.7)=(1426.3,\ 1509.7)[/tex]
