Respuesta :
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 [tex]$(Bq/m^3)$[/tex]. For this data, assume that [tex]$\bar x =3,751 \ Bq/m^3$[/tex] and [tex]$s= 1,259 \ Bq/m^3.$[/tex]. 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, [tex]$\bar x =3,751 \ Bq/m^3$[/tex]
Mean standard deviation , [tex]$s= 1,259 \ Bq/m^3.$[/tex].
Sample size, n = 12
∴ Degree of freedom = n-1 = 12-1
= 11
Significance level, α = 0.05
The critical level, [tex]$t^*_{n-1} = 2.201$[/tex]
Therefore, lower limit = [tex]$\bar x - t^*_{n-1} \left(\frac{s}{\sqrt n}\right)$[/tex]
[tex]$= 3751 - 2.201 \left(\frac{1259}{\sqrt {12}}\right)$[/tex]
= 2951
Upper Limit = [tex]$\bar x + t^*_{n-1} \left(\frac{s}{\sqrt n}\right)$[/tex]
[tex]$= 3751 + 2.201 \left(\frac{1259}{\sqrt {12}}\right)$[/tex]
= 4551
Therefore the confidence interval is with 95 % and the true mean level of radon exposure in the tombs is between 2951 [tex]$Bq/m^3$[/tex] and 4551 [tex]$Bq/m^3$[/tex] .
