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 / m ^ 3 ). For this​ data, assume that x = 3,457 Bq/m^3 and s = 1,282 Bq/m^3. Use this information to​ estimate, with 95​% ​confidence, the true mean level of radon exposure in tombs in the region. Interpret the resulting interval.

The confidence interval is ( ________, ________ ).

Answer 1

sample mean, xbar = 3457
sample standard deviation, s = 1282
sample size, n = 12
degrees of freedom, df = n - 1 = 11

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.201

ME = tc * s/sqrt(n)
ME = 2.201 * 1282/sqrt(12)
ME = 814.549

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (3457 - 2.201 * 1282/sqrt(12) , 3457 + 2.201 * 1282/sqrt(12))
CI = (2642.5 , 4271.5)