20. (12 points)\\
A medical team conducted a study on the relationship between a certain endemic disease in a region and the hygiene habits of local residents (hygiene habits are classified as either good or not sufficiently good). Among patients with the disease, 100 cases were randomly surveyed (called the case group), and among people without the disease, 100 people were randomly surveyed (called the control group). The following data were obtained:

\begin{center}
\begin{tabular}{ | c | c | c | l | }
\hline
 & Not Sufficiently Good & Good &  \\
\hline
Case Group & 40 & 60 &  \\
\hline
Control Group & 10 & 90 &  \\
\hline
\end{tabular}
\end{center}

(1) Can we conclude with 99\% confidence that there is a difference in hygiene habits between the group with the disease and the group without the disease?\\
(2) From the population of the region, one person is randomly selected. Let $A$ denote the event ``the selected person has not sufficiently good hygiene habits'' and $B$ denote the event ``the selected person has the disease''. The ratio $\frac { P ( B \mid A ) } { P ( \bar { B } \mid A ) }$ to $\frac { P ( B \mid \bar { A } ) } { P ( \bar { B } \mid \bar { A } ) }$ is a measure of the risk level of the disease associated with not sufficiently good hygiene habits. Let this measure be denoted as $R$.\\
(i) Prove that $R = \frac { P ( A \mid B ) } { P ( \bar { A } \mid B ) } \