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

Answer 1

The question is incomplete. The complete question is :

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
`$\bar x =3,751 \ Bq/m^3$` and
`$s= 1,259 \ Bq/m^3.$`. Use this information to​ estimate, with 95% confidence, the mean level of radon exposure in tombs in the region. Interpret the resulting interval.

Solution :

Here, given

Mean sample,
`$\bar x =3,751 \ Bq/m^3$`

Mean standard deviation ,
`$s= 1,259 \ Bq/m^3.$`.

Sample size, n = 12

∴ Degree of freedom = n-1 = 12-1

= 11

Significance level, α = 0.05

The critical level,
`$t^*_(n-1) = 2.201$`

Therefore, lower limit =
`$\bar x - t^*_(n-1) \left((s)/(\sqrt n)\right)$`

`$= 3751 - 2.201 \left(\frac{1259}{\sqrt {12}}\right)$`

= 2951

Upper Limit =
`$\bar x + t^*_(n-1) \left((s)/(\sqrt n)\right)$`

`$= 3751 + 2.201 \left(\frac{1259}{\sqrt {12}}\right)$`

= 4551

Therefore the confidence interval is with 95 % and the true mean level of radon exposure in the tombs is between 2951
`$Bq/m^3$` and 4551
`$Bq/m^3$` .