Question

The anterior cruciate ligament (ACL) runs diagonally in the middle of the knee. An article reported results for 85 young athletes who suffered anterior cruciate ligament (ACL) injuries. Of the 85 injuries, 53 were to the left knee and 32 were to the right knee. Can you conclude that more than half of ACL injuries are to the left knee? Find the P-value and state a conclusion.

Answer 1

The left knee injuries are more than half.

Explanation:

Given that the anterior cruciate ligament (ACL) runs diagonally in the middle of the knee.

Sample size n = 85

left knee = 53

p = Sample proportion =
`(53)/(85) \\=0.624`

`H_0: p = 0.5\\H_a: p>0.5`

(Right tailed test)

p difference = 0.124

std error =
`\sqrt{(0.5(0.5))/(85) } \\=0.0542`

Test statistic z = 2.28

p value = 0.01130

Since p <0.05, at 5% level we reject H0.

The left knee injuries are more than half.