Some sports that involve a significant amount of running, jumping, or hopping put participants at risk for Achilles tendon injuries. A study looked at the diameter (in mm) of the injured tendons for patients who participated in these types of sports activities. Suppose that the Achilles tendon diameters in the general population have a mean of5.98millimeters(mm). When the diameters of the injured tendon were measured for a random sample of32patients,the average diameter was9.70mmwith a standard deviation of1.94mm. Is there sufficient evidence to indicate that the average diameter of the tendon for patients with Achilles tendon injuries is greater than5.98mm?Test at the5% levelof significance.

State the null and alternative hypotheses.

H₀:< 5.98 versusH_a:> 5.98

H₀:= 5.98 versusH_a:5.98

H₀:= 5.98 versusH_a:> 5.98

H₀:5.98 versusH_a:= 5.98

H₀:= 5.98 versusH_a:< 5.98

Find the test statistic and rejection region. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.)

test statisticz=rejection regionz>z<

State your conclusion.

H₀is rejected. There is insufficient evidence to indicate that the average diameter of the tendon for patients with AT is greater than 5.98 mm.

H₀is not rejected. There is insufficient evidence to indicate that the average diameter of the tendon for patients with AT is greater than 5.98 mm.

H₀is not rejected. There is sufficient evidence to indicate that the average diameter of the tendon for patients with AT is greater than 5.98 mm.

H₀is rejected. There is sufficient evidence to indicate that the average diameter of the tendon for patients with AT is greater than 5.98 mm.

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