### Radon Levels in Ancient TombsMany 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 ( $ \text{Bq/m}^3 $ ). For this data, assume that $ \overline{x} = 3,688 \text{ Bq/m}^3 $ and $ s = 1,218 \text{ Bq/m}^3 $. Use this information to estimate, with 95% confidence, the true mean level of radon exposure in tombs in the region. Interpret the resulting interval. Assume that the sampled population is approximately normal.#### The confidence interval is \[ \left( \boxed{} \, , \, \boxed{} \right) \]*(Round to the nearest integer as needed.)*---In this study, the sample mean ($ \overline{x} $) and the sample standard deviation ($ s $) are given. To calculate the 95% confidence interval for the true mean radon level, use the formula for the confidence interval of the mean for normally distributed data:\[ \overline{x} \pm t_{\frac{\alpha}{2}} \times \frac{s}{\sqrt{n}} \]Where:- $ \overline{x} $ is the sample mean- $ t_{\frac{\alpha}{2}} $ is the critical value from the t-distribution- $ s $ is the sample standard deviation- $ n $ is the sample sizeFor a 95% confidence level and a sample size of 12, the degrees of freedom (df) will be $ n-1 = 11 $. The critical t-value for 11 degrees of freedom at the 95% confidence level can be found using t-distribution tables or software.

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Description: ### Radon Levels in Ancient TombsMany 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 particula

In question, We have given sample of size 12 and sample mean 3688 Bq/m^3 and sample standard…

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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). For this data, assume that x = 3,688 Bq/ m° and s = 1,218 Bq/m. Use this information to estimate, with 95% confidence, the true mean level of radon exposure in tombs in the region. Interpret the resulting interval. Assume that the sampled population is approximately normal. The confidence interval is ( D (Round to the nearest integer as needed.)

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). For this data, assume that x = 3,688 Bq/ m° and s = 1,218 Bq/m. Use this information to estimate, with 95% confidence, the true mean level of radon exposure in tombs in the region. Interpret the resulting interval. Assume that the sampled population is approximately normal. The confidence interval is ( D (Round to the nearest integer as needed.)

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### Radon Levels in Ancient Tombs

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 ( $ \text{Bq/m}^3 $ ). For this data, assume that $ \overline{x} = 3,688 \text{ Bq/m}^3 $ and $ s = 1,218 \text{ Bq/m}^3 $.

Use this information to estimate, with 95% confidence, the true mean level of radon exposure in tombs in the region. Interpret the resulting interval. Assume that the sampled population is approximately normal.

#### The confidence interval is
\[ \left( \boxed{} \, , \, \boxed{} \right) \]
*(Round to the nearest integer as needed.)*

---

In this study, the sample mean ($ \overline{x} $) and the sample standard deviation ($ s $) are given. To calculate the 95% confidence interval for the true mean radon level, use the formula for the confidence interval of the mean for normally distributed data:
\[ \overline{x} \pm t_{\frac{\alpha}{2}} \times \frac{s}{\sqrt{n}} \]

Where:
- $ \overline{x} $ is the sample mean
- $ t_{\frac{\alpha}{2}} $ is the critical value from the t-distribution
- $ s $ is the sample standard deviation
- $ n $ is the sample size

For a 95% confidence level and a sample size of 12, the degrees of freedom (df) will be $ n-1 = 11 $. The critical t-value for 11 degrees of freedom at the 95% confidence level can be found using t-distribution tables or software.

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