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 x̄ = 3,778 Bq / m³ and s = 1,154 Bq / m³ . Use this information to​ estimate, with 95​% ​confidence, the true mean level of radon exposure in tombs in the region. Interpret the resulting interval.

A) The confidence interval is ( ___ , ___ ) * round to the nearest integer as needed

Answer 1

Solution :

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

t/2,df = t0.025,11 = 2.201

Margin of error = E = t/2,df * (s /n)

= 2.201 * ( 1154/ 12)

Margin of error = E = 733

The 95% confidence interval estimate of the population mean is,

  ± E

= 3778   ± 733

= ( 3045, 4511 )

We are 95% confident that the true mean level of radon exposure in tombs in the region between 3045 Bq / m³ and 4511 Bq / m³