Question

Many ancient tombs were cut from limestone rock that contained uranium. Since most such tombs are not​ well-ventilated, they may contain radon gas. In one​ study, the radon levels in a sample of 12 tombs in a particular region were measured in becquerels per cubic meter (Bq/m3). For this​ data, assume that x(over-bar)= 3,469 Bq/m3 and s= 1,135 Bq/m3. Use this information to​ estimate, with 95% confidence, the mean level of radon exposure in tombs in the region. Interpret the resulting interval.

Answer 1

95% confidence interval of the mean level of random exposure in tombs in the region.

(2746.868 , 4191.132)

Explanation:

Step(i):-

Given sample size 'n'= 12

Mean of the sample x⁻ = 3,469

and standard deviation of the sample 's' = 1,135

95% confidence intervals are determined by

`(x^(-) - t_(0.05) (S)/(√(n) ) , x^(-) +t_(0.05) (S)/(√(n) ) )`

Degrees of freedom = n-1 = 12-1= 11

Step(ii):-

95% confidence intervals are determined by

`(3469- 2.201 (1135)/(√(12) ) , 3469+2.201(1135)/(√(12) ) )`

( 3469-722.132 , 3469 +722.132)

(2746.868 , 4191.132)