Radon exposure in Egyptian tombs. Many ancient Egyptian tombs were cut from limestone rock that contained uranium. Since most tombs are not well ventilated, guards, tour guides, and visitors may be exposed to deadly

radon gas. In Radiation Protection Dosimetry(December 2010), a study of radon exposure in tombs in the Valley of Kings, Luxor, Egypt (recently opened for public tours), was conducted. The radon levels—measured in becquerels

per cubic meter (\({\bf{Bq/}}{{\bf{m}}^{\bf{3}}}\))—in the inner chambers of a sample of 12 tombs were determined. Summary statistics follow:\({\bf{\bar x}}\)= 3,643\({\bf{Bq/}}{{\bf{m}}^{\bf{3}}}\)and s= 4,487\({\bf{Bq/}}{{\bf{m}}^{\bf{3}}}\). Use this information to estimate, with 95% confidence, the true mean level of radon exposure in tombs in the Valley of Kings. Interpret the resulting interval.

There is a study about radon exposure in tombs in the valley of kings, Luxor, Egypt. There are some data about 12 tombs and their radon levels. The summary is \(\bar x = 3643\) and the standard deviation \(s = 4487\).

The confidence interval is\(\left( {\bar x \pm {t_{\frac{\alpha }{2},\left( {n - 1} \right)}} \times \frac{s}{{\sqrt n }}} \right)\).

Now,the confidence interval is 95%.

Therefore, the level of significance\(\alpha = 1 - 0.95 = 0.05\).

So, from the t-table, the statistic\({t_{\frac{\alpha }{2},\left( {n - 1} \right)}} = {t_{0.025,11}} = 2.201\).

Thus,

\(\begin{aligned}\left( {\bar x \pm {t_{\frac{\alpha }{2},\left( {n - 1} \right)}} \times \frac{s}{{\sqrt n }}} \right) &= \left( {3643 \pm {t_{0.025,11}} \times \frac{{4487}}{{\sqrt {12} }}} \right)\\ &= \left( {\left( {3643 - 2.201 \times 1295.28} \right),\left( {3643 + 2.201 \times 1295.28} \right)} \right)\\ &= \left( {792.08,6493.91} \right)\end{aligned}\)

Thus, the 90% confidence interval is (792.08,6493.91).