Question

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 32 patients, the average diameter was 9.50 with a standard deviation of 1.96 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.

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 <

Answer 1

Null Hypothesis, 5.95

Alternative Hypothesis, 5.95

xbar = 9.5, s = 1.96, n = 32

Test statistic,
z = (9.5 - 5.95)/(1.96/sqrt(32))
z = 10.25

Here the significance level, 0.05.

This is right tailed test; hence rejection region lies to the right.

1.64 i.e. P(z > 1.64) = 0.05

Rejection region: reject H0 if z > 1.64

z < none

Reject H0 as test statistic is greater than 1.64

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