## Elementary Statistics: A Step-by-Step Approach with Formula Card 9th Edition

$P_{f}=79.3\%$ $P_{m}=21.7\%$ a. No. b. there were at least 644 male players.
Among these 46 ACL tears cases, 36 were female and 10 were male. The percentage of female among these 46 cases is: $P_{f}=\frac{36}{46}=79.3\%$ Similarly, the the percentage of male among these 46 cases is: $P_{m}=\frac{10}{46}=21.7\%$ a. We can not conclude that female athletes tear their knees more often than male athletes. This is because we need the number of total female (or male) in the 2958 players. It could happen that there were only a small number of male players (say 20) and $P_{m}$ becomes $\frac{10}{20}=50\%$ while $P_{f}=\frac{36}{2958-20}=1.2\%$ for each individual groups. b. To reach a conclusion that female athletes tear their knees more often than male athletes, we need to make an assumption that among the total 2958 players, there were at least 644 male players. At this limit, $P_{m}=\frac{10}{644}=1.553\%$, while $P_{f}=\frac{36}{2958-644}=1.556\%$ for each individual group.