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.

1. Calculate the values of \(A , B , C\) in the tables below.

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

   \multirow{2}{*}{}	\multirow[b]{2}{*}{Chi-Squared Contributions}	Site of injury
   		Shoulder/ Arm	Hand/ Fingers	Thigh/ Leg	Knee	Ankle	Foot	Other
   \multirow{3}{*}{sodoct}	Football	1.98732	23.03890	\(10 \cdot 77575\)	2.47484	\(B\)	9.47586	0.31575
   	Handball	4.73333	4.38079	C	0.17087	1.44690	3.80664	0.73331
   	Basketball	0.20286	26.38865	4.10400	4.10400	0.00102	6.40306	3.93521

2. Given that the test statistic, \(X ^ { 2 }\), is 116.16, carry out the significance test at the \(5 \%\) level.
3. 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.

   Observed values	Ball	Opponent	Surface	None	Total
   Football	17	68	17	92	194
   Handball	23	34	19	38	114
   Basketball	28	17	12	14	71
   Total	68	119	48	144	379

   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).
4. State Rhian's misconception and explain what she should consider instead. \section*{END OF PAPER}