7. An article published in a medical journal investigated sports injuries in adolescents' ball games: football, handball and basketball. In a study of 906 randomly selected adolescent players in the three ball games, 379 players incurred injuries over the course of one year of playing the sport. Rhian wants to test whether there is an association between the site of injury and the sport played. A summary of the injuries is shown in the table below.

\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|}
\hline
\multirow{2}{*}{} &  & \multicolumn{7}{|c|}{Site of injury} &  \\
\hline
 & Observed values & Shoulder/ Arm & Hand/ Fingers & Thigh/ Leg & Knee & Ankle & Foot & Other & Total \\
\hline
\multirow{3}{*}{Sport} & Football & 8 & 3 & 45 & 36 & 51 & 36 & 12 & 191 \\
\hline
 & Handball & 14 & 26 & 6 & 15 & 42 & 6 & 6 & 115 \\
\hline
 & Basketball & 4 & 28 & 4 & 4 & 22 & 1 & 10 & 73 \\
\hline
 & Total & 26 & 57 & 55 & 55 & 115 & 43 & 28 & 379 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Calculate the values of $A , B , C$ in the tables below.

\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|l|l|}
\hline
\multirow{2}{*}{} &  & \multicolumn{7}{|c|}{Site of injury} \\
\hline
 & Expected values & Shoulder/ Arm & Hand/ Fingers & Thigh/ Leg & Knee & Ankle & Foot & Other \\
\hline
\multirow{3}{*}{sodod} & Football & 13.1029 & 28.7256 & 27.7177 & 27.7177 & 57.9551 & 21.6702 & 14.1108 \\
\hline
 & Handball & 7.8892 & 17.2955 & 16.6887 & 16.6887 & A & 13.0475 & 8.4960 \\
\hline
 & Basketball & 5.0079 & 10.9789 & 10.5937 & 10.5937 & 22.1504 & 8.2823 & 5.3931 \\
\hline
\end{tabular}
\end{center}

\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|l|l|}
\hline
\multirow{2}{*}{} & \multirow[b]{2}{*}{Chi-Squared Contributions} & \multicolumn{7}{|c|}{Site of injury} \\
\hline
 &  & Shoulder/ Arm & Hand/ Fingers & Thigh/ Leg & Knee & Ankle & Foot & Other \\
\hline
\multirow{3}{*}{sodoct} & Football & 1.98732 & 23.03890 & $10 \cdot 77575$ & 2.47484 & $B$ & 9.47586 & 0.31575 \\
\hline
 & Handball & 4.73333 & 4.38079 & C & 0.17087 & 1.44690 & 3.80664 & 0.73331 \\
\hline
 & Basketball & 0.20286 & 26.38865 & 4.10400 & 4.10400 & 0.00102 & 6.40306 & 3.93521 \\
\hline
\end{tabular}
\end{center}
\item Given that the test statistic, $X ^ { 2 }$, is 116.16, carry out the significance test at the $5 \%$ level.
\item Which site of injury most affects the conclusion of this test? Comment on your answer.

Rhian also analyses the data on the type of contact that caused the injuries and the sport in which they occur, shown in the table below.

\begin{center}
\begin{tabular}{|l|l|l|l|l|l|}
\hline
Observed values & Ball & Opponent & Surface & None & Total \\
\hline
Football & 17 & 68 & 17 & 92 & 194 \\
\hline
Handball & 23 & 34 & 19 & 38 & 114 \\
\hline
Basketball & 28 & 17 & 12 & 14 & 71 \\
\hline
Total & 68 & 119 & 48 & 144 & 379 \\
\hline
\end{tabular}
\end{center}

The chi-squared test statistic is 46.0937 . Rhian notes that this value is smaller than 116.16 , the test statistic in part (b). She concludes that there is weaker evidence for association in this case than there was in part (b).
\item State Rhian's misconception and explain what she should consider instead.

\section*{END OF PAPER}
\end{enumerate}

\hfill \mbox{\textit{WJEC Further Unit 2 2019 Q7 [13]}}