Question

An article in Knee Surgery, Sports Traumatology, Arthroscopy (2005, Vol. 13, pp. 273–279), considered arthroscopic meniscal repair with an absorbable screw. Results showed that for tears greater than 25 millimeters, 14 of 18 (78%) repairs were successful while for shorter tears, 22 of 30 (73%) repairs were successful.

What would be the result of making a type II error in this case?
Is there evidence that the success rate is greater for longer tears? Use α = 0.05.

Answer 1

A type II error in this case would be failing to reject the null hypothesis when it is actually false.

To determine if there is evidence that the success rate is greater for longer tears, we can conduct a hypothesis test. Using α = 0.05, if the p-value is less than 0.05, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the success rate is greater for longer tears.

A type II error in this case would be failing to reject the null hypothesis when it is actually false.

In other words, it would mean concluding that there is no evidence that the success rate is greater for longer tears, when in fact there is.

This error would result in missed opportunities for further investigation or treatment of longer tears.

To determine if there is evidence that the success rate is greater for longer tears, we can conduct a hypothesis test. The null hypothesis (H0) would be that the success rate is the same for tears of all lengths, while the alternative hypothesis (Ha) would be that the success rate is greater for longer tears.

Using α = 0.05, we compare the p-value to the significance level.

If the p-value is less than 0.05, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the success rate is greater for longer tears.