Question

ACL injuries. What hypotheses reflect the research hypothesis that the proportion of ACL injuries to the right knee is different from 0.50? Let ( p ) be the proportion of ACL injuries that are to the right knee in the population.

a) ( H_0: p = 0.50 ), ( H_a: p neq 0.50 )
b) ( H_0: p neq 0.50 ), ( H_a: p = 0.50 )
c) ( H_0: p > 0.50 ), ( H_a: p ≤ 0.50 )
d) ( H_0: p ≤ 0.50 ), ( H_a: p > 0.50 )

Answer 1

The hypotheses that best reflect the research hypothesis for a different proportion from 0.50 of right knee ACL injuries are H0: p = 0.50 and Ha: p ≠ 0.50, defining a two-tailed test.

Step-by-step explanation:

The research hypothesis that the proportion of ACL injuries to the right knee is different from 0.50 is reflected in the hypothesis pair:

• H0: p = 0.50
• Ha: p ≠ 0.50

This is a two-tailed test because the research hypothesis is interested in any difference from 0.50, whether it is greater than or less than. The null hypothesis (H0) states that there is no difference, and the alternative hypothesis (Ha) that the proportion is not equal to 0.50 indicates the potential for a difference in the proportion of right knee ACL injuries from the expected rate of 0.50.