Question

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. Which interval is the 90% confidence interval for the mean square footage of all homes in that city?

Answer 1

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

$90\%\ C.1.=\bar{x}\pm1.65\left( \frac{\sigma}{\sqrt{n}} \right) \\ \\ =1468\pm1.65\left( \frac{213}{\sqrt{71}} \right)=1468\pm1.65(25.28) \\ \\ =(1468-41.7,\ 1468+41.7)=(1426.3,\ 1509.7)$