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 tendon diameters in the general population have a mean of 5.97 millimeters (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 were measured for a sample of 31 patients, the average diameter was 9.80. 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 probability of observing an average diameter of 9.80 or higher?
c. What conclusions might you draw from the results of part b?