Question

Radon is a colorless and odorless radioactive gas that can accumulate in residential homes. High levels of exposure can lead to health problems. Radon levels are measured in units of picocuries per liter pCi/L. The recommended radon level is less than 4 pCi/L. A housing development has 125 residential homes. The homeowners association would like to estimate the average radon level in the development. Because it would be too expensive to measure every​ home, a random sample of 35 homes was selected to be​ tested, and the average radon level was found to be 2.1 pCi/L. Assume from past studies the population standard deviation of radon levels in homes is 0.6 pCi/L. Complete parts a and b below.

a. Construct a​ 90% confidence interval to estimate the average radon level in the housing development.

The​ 90% confidence interval to estimate the average radon level is (___ pCi/L, ___ pCi/L).

Answer: The 90% confidence interval to estimate the average radon level is (1.96 pCi/L, 2.24 pCi/L).

b. Does it appear the average radon level is below the​ recommendation?

Answer: Compare the confidence interval to the maximum recommended radon level. If the confidence interval contains 4 pCi/L​, or if 4 pCi/L is less than all the values in the confidence​ interval, there is insufficient evidence that the average radon level is below the recommendation.

Above are the questions and answers. Please provide all Excel formulas (not calculations) that get to these answers.

Answer 1

Solution-A:

margin of error in excel

=CONFIDENCE.NORM(0.1,0.6,35)

=

0.166819

lower limit=xbar-MOE=2.1-0.166819= 1.933181=1.93

upper limit=xbar+MOE=2.1+0.166819=2.26681=2.27

Solution-b:

Ho:mu=4

Ha:mu<4

since the 90% confidence interval for mean is (1.93,2.27) ,hypothesized mean 4 is not included in the interval

Reject Ho

Accept Ha

, there is sufficient evidence that the average radon level is below the recommendation.