Question

Radon is a colorless and odorless radioactive gas that can accumulate in residential homes. High levels of exposu is less than 4 pCi/L. A housing development has 108 residential homes. The homeowners association would like sample of 26 homes was selected to be tested, and the average radon level was found to be 1.5 pCi/L. Assume fr 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) (Round to two decimal places as needed.) b. Does it appear the average radon level is below the recommendation? O A. No, because some of the values in the confidence interval are greater than 4 pCi/L OB. Yes, because all the values in the confidence interval are less than 4 pCi/L. OC. Yes, because 4 pCi/L is contained in the confidence interval. OD. No, because 4 pCl/L is contained in the confidence interval.

Answer 1

Solution :

Given that,

Point estimate = sample mean = $\bar x$ = 1.5

Population standard deviation =   $\sigma$ = 0.5

Sample size = n = 26

At 90% confidence level

$\alpha$ = 1 - 90%  

$\alpha$ = 1 - 0.90 =0.10

$\alpha$/2 = 0.05

Z$\alpha$/2 = Z_{0.05 = 1.645}

_{a) The 90% confidence interval is}

_{X+-Z*S/sq(n) =1.5+-1.645*0.5/sq(26)}

_{= ( 1.339, 1.661)}

_{90%CI = ( 1.34, 1.66)}

_b)

Yes, because all the value in the confidence interval are less than 4pCi/L

Option B is correct

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