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\pageheader{Mathematical Sciences 302 - Statistics for Science and 
Engineering}{}{Case Study I}
\pagefooter{Department of Mathematical 
Sciences - Clemson University}{}{Calvin L. Williams, Ph.D.}
\begin{document}
\begin{center}
{\Large \bf Mathematical Sciences 302 \\ Case Study: Environmental 
Engineering\\ Radon Gas Emissions}
\end{center}
Much research has been conducted during the past
 few years in an attempt to understand the health effects of radon 
 gas in dwellings. Radon is a radioactive gas that is generally 
 present in harmless amounts in nature. However, in certain
 dwellings radon gas is known to be present in quantities 
 that may be harmful to humans particularly in basements of
 buildings where the air is stagnant. The Environmental 
 Protection Agency (EPA) sets standards for environmental
 emissions from hazardous substances. According to the July
 1995 issue of Consumer Reports, the EPA has suggested that
 radon levels exceeding 4.0 pc/l picocurie per liter,
 which is a measure of radioactive emissions) are associated
 with an increased risk of lung cancer. Although this is debatable,
 there seems to be a general belief among scientists that radon 
 levels above 16.0 pc/l pose a serious health threat. A real 
 estate developer owns 51 residential buildings that he wants
 to sell. Before the buildings can be sold, the radon level
 in each building must be determined. If it exceeds 4.0 pc/l 
 in any building, the buyer must be so advised. It it exceeds
 16.0 pc/l in any building, some corrective measures must be 
 taken. 
\begin{description}% Level I 
\item \question : Describe these set of observations by a 
numerical summary that would include measures of central tendency 
such as: the mean, median, and the mode. Also include measures of
dispersion such as the variance, the standard
deviation, and the range.

\item \question : Describe these set of observations by:(i) a 
step-and-leaf plot, and (ii) a relative frequency histogram.


 Another question of interest in the investigation is the
 following.

 \item \question: For what percentage of the 51 residential
buildings does radon present a potential health problem? 
Specifically, what percentage of the 51 residential 
buildings has a radon level exceeding 4.0 but less than 
or equal to 16.0 pc/l, and what percentage of the buildings 
has a radon level exceeding 6.0 pc/l~?
\end{description}
\pagebreak
\begin{table}[h]
\begin{tabular}{ccccccc}
& & Radon & Radon & Radon\\
&Building & concentration & Building & concentration & Building & 
concentration\\
&number & (in pc/l) & number & (in pc/l) & number & (in pc/l) \\ \hline
 & 1 & 13.6 & 18 & 2.9 & 35 & 6.5\\
 & 2 & 2.8 & 19 & 2.0 & 36 & 11.8\\
 & 3 & 2.9 & 20 & 2.9 & 37 & 13.2\\
 & 4 & 3.8 & 21 & 11.2 & 38 & 2.8\\
 & 5 & 15.9 & 22 & 1.9 & 39 & 6.9\\
 & 6 & 1.7 & 23 & 2.0 & 40 & 0.7\\
 & 7 & 3.4 & 24 & 6.0 & 41 & 12.9\\
 & 8 & 13.7 & 25 & 2.9 & 42 & 3.6\\
 & 9 & 6.1 & 26 & 7.7 & 43 & 3.6\\
 & 10 & 16.8 & 27 & 5.1 & 44 & 8.1\\
 & 11 & 7.9 & 28 & 13.2 & 45 & 17.0\\
 & 12 & 3.5 & 29 & 3.8 & 46 & 8.2\\
 & 13 & 2.2 & 30 & 13.9 & 47 & 9.8\\
 & 14 & 4.1 & 31 & 2.4 & 48 & 13.0\\
 & 15 & 3.2 & 32 & 7.9 & 49 & 11.3\\
 & 16 & 2.9 & 33 & 1.4 & 50 & 4.0\\
 & 17 & 3.7 & 34 & 5.9 & 51 & 6.0\\ \hline \hline
 &\multicolumn{6}{c}{ Ordered radon measures}\\ \hline \hline
% \end{tabular}
% \end{table}
% \begin{table}[h]
% \begin{tabular}{ccccccc}
% & & Radon & Radon & Radon\\
% &Building & concentration & Building & concentration & Building & 
% concentration\\
% &number & (in pc/l) & number & (in pc/l) & number & (in pc/l) \\ \hline
 & 40 & 0.7 & 12 & 3.5 & 32 & 7.9\\
 & 33 & 1.4 & 42 & 3.6 & 44 & 8.1\\
 & 6 & 1.7 & 43 & 3.6 & 46 & 8.2\\
 & 22 & 1.9 & 17 & 3.7 & 47 & 9.8\\
 & 19 & 2.0 & 4 & 3.8 & 21 & 11.2\\
 & 23 & 2.0 & 29 & 3.8 & 49 & 11.3\\
 & 13 & 2.2 & 50 & 4.0 & 36 & 11.8\\
 & 31 & 2.4 & 14 & 4.1 & 41 & 12.9\\
 & 2 & 2.8 & 27 & 5.1 & 48 & 13.0\\
 & 38 & 2.8 & 34 & 5.9 & 28 & 13.2\\
 & 3 & 2.9 & 24 & 6.0 & 37 & 13.2\\
 & 16 & 2.9 & 51 & 6.0 & 1 & 13.6\\
 & 18 & 2.9 & 9 & 6.1 & 8 & 13.7\\
 & 20 & 2.9 & 35 & 6.5 & 30 & 13.9\\
 & 25 & 2.9 & 39 & 6.9 & 5 & 15.9\\
 & 15 & 3.2 & 26 & 7.7 & 10 & 16.8\\
 & 7 & 3.4 & 11 & 7.9 & 45 & 17.0 \\ \hline \hline
 \end{tabular}
 \end{table}
\end{document}
