\begin{table}%t3
%\centering
\par
\caption{\label{Tab:hyper}Results of a hypergeometric test checking the $H_0$ hypothesis that the
frequency $p$ of stars above the dividing line is the same on both sides
of the $Sb$ threshold value.}
%\centerline
{\small \begin{tabular}{llrrrrrrrr}
\hline \hline\noalign{\smallskip}
Case    &  $Sb$  & $\sigma_0 > 3$ & $\sigma_0 \le 3$ &  $N_i$& $p_i =x_i/N_i$ & $\tilde{x_1}$ & $\sigma_{x1}$ & $c^2$\phantom{1} & $\alpha$\\
\hline
Sample I & $\ge$4.5  & $x_1 =\phantom{1} 5^a$   &  154 &  159 & 0.031 & 5.77 & 2.03 & 0.145 & 0.35\\
 & $<$4.5  & $x_2 = 17$  &  430 &  447 & 0.038  \\
  & All  & $x_3 = 22$  &  584 &  606 & 0.036  \\
Sample I & $\ge$5.0  & 3   &  104 &  107 & 0.028 & 3.88 & 1.76 & 0.253 & 0.31\\
         & $<$5.0     & 19  &  480 &  499 & 0.038  \\
         & All        & 22  &  584 &  606 & 0.036  \\
Sample I & $\ge$6.0  & 3   &   60 &   63 & 0.048 & 2.29 & 1.41 & 0.257 & 0.31\\
         & $<$6.0     & 19  &  524 &  543 & 0.035 & \\
         & All        & 22  &  584 &  606 & 0.036  \\
\hline
         &            & $\sigma_0 >  0.57 Sb$ & $\sigma_0 \le 0.57 Sb$ \\ 
%\hline
Sample I & $\ge$5.0  & 2   &  105 &  107 & 0.019 & 6.36 & 2.22 & 3.85 & 0.025\\
         & $<$5.0     & 34  &  465 &  499 & 0.068  \\
         & All        & 36  &  570 &  606 & 0.059  \\
\hline
         &            & $\sigma_0 >  0.23 Sb + 0.2$ & $\sigma_0 \le 0.23 Sb+0.2$ \\ 
%\hline
Sample II& $\ge$5.0  & 1   &   28 &   29 & 0.034 & 3.43 & 1.64 & 2.189 & 0.069\\
         & $<$5.0     & 29  &  196 &  225 & 0.129  \\
         & All        & 30  &  224 &  254 & 0.118                   \\
\hline
\end{tabular}}
\medskip
$^a$ Subscripts~1, 2, and~3 denote quantities for stars above the dividing line, below it, and the total number, respectively. 
\end{table}