Question

# Some sports that involve a significant amount of running, jumping, or hopping put participants at risk...

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 looked at the diameter (in mm) of the 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 5.95 millimeters (mm). When the diameters of the affected tendon were measured for a random sample of 34 patients, the average diameter was 9.50 with a standard deviation of 1.98 mm. Is there sufficient evidence to indicate that the average diameter of the tendon for patients with AT is greater than 5.95 mm? Test at the 5% level of significance.

State the null and alternative hypotheses.

H0: μ < 5.95 versus Ha: μ > 5.95

H0: μ = 5.95 versus Ha: μ > 5.95

H0: μ = 5.95 versus Ha: μ ≠ 5.95

H0: μ ≠ 5.95 versus Ha: μ = 5.95

H0: μ = 5.95 versus Ha: μ < 5.95

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 statistic z =

rejection region

z >

z <

H0 is rejected. There is insufficient evidence to indicate that the average diameter of the tendon for patients with AT is greater than 5.95 mm. H0 is not rejected. There is insufficient evidence to indicate that the average diameter of the tendon for patients with AT is greater than 5.95 mm.

H0 is not rejected. There is sufficient evidence to indicate that the average diameter of the tendon for patients with AT is greater than 5.95 mm.

H0 is rejected. There is sufficient evidence to indicate that the average diameter of the tendon for patients with AT is greater than 5.95 mm.

Solution:
Null hypothesis is H0: mean = 5.95
Alternate hypothesis is H1: mean > 5.95
test statistic = (9.5-5.95)/1.98/sqrt(34) = 10.45
at alpha = 0.05 this is a right tailed test so Z at 0.05 is 1.645
If test statistic is greater than 1.645 than reject null hypothesis else do not reject the null hypothesis.
As we can see that Ztest>1.645, So H0 is rejected. there is sufficient evidence to indicate that the average diameter of the tenfon for patients with AT is greater than 5.595 mm.

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