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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).