7.40 Sports and Achilles Tendon Injuries Some sports that involve a significant amount of running, jumping, or hopping put participants at risk for Achilles tendinopathy (AT), an inflammation and thickening of the Achilles tendon. A study in The American Journal of Sports Medicine looked at the diameter (in mm) of the affected and non-affected tendons for patients who participated in these types of sports activities. Suppose that the Achilles ten- don diameters in the general population have a mean of 5.97 millimetres (mm) with a standard deviation of 1.95 mm.

a. What is the probability that a randomly selected sample of 31 patients would produce an average diameter of 6.5 mm or less for the non-affected tendon?

b. When the diameters of the affected tendon was measured for a sample of 31 patients, the aver- age diameter was 9.80 mm. If the average tendon diameter in the population of patients with AT is no different than the average diameter of the non-affected tendons (5.97 mm), what is the prob- ability of observing an average diameter of 9.80 mm or higher?

c. What conclusions might you draw from the results of part b?