Radon is a colorless and odorless radioactive gas that can accumulate in residential homes. High levels of exposure can lead to health problems such as lung cancer. Radon levels are measured in units of picocuries per liter (pCi/ L). The recommended radon level from the EPA is less than 4 pCi/L. Taylor Mill is a housing development with 105 residential homes. The development’s homeowners association would like to estimate the average radon level in the development’s homes. Because it would be too expensive to measure every home, a random sample of 32 homes was selected to be tested, and the average radon level was found to be 1.4 pCi/ L. Assume from past studies, the population standard deviation of radon levels in homes is 0.5 pCi/ L.

a. Construct a 95% confidence interval to estimate the average radon level in the Taylor Mill development.

b. Does it appear the average radon level is below the EPA’s recommendation?

c. Verify your results using PHStat.