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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 5.97 millimeters (mm). When the diameters of the affected tendon were measured for a random sample of 31 patients, the average diameter was 9.70 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 5.97 mm? Test at the 5% level of significance.

State the null and alternative hypotheses.

H0: μ = 5.97 versus Ha: μ > 5.97

H0: μ = 5.97 versus Ha: μ < 5.97

H0: μ = 5.97 versus Ha: μ ≠ 5.97

H0: μ ≠ 5.97 versus Ha: μ = 5.97

H0: μ < 5.97 versus Ha: μ > 5.97

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 rejection region

z=

z >

z <

State your conclusion.

H0 is rejected. There is sufficient evidence to indicate that the average diameter of the tendon for patients with AT is greater than 5.97 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 5.97 mm.

H0 is rejected. There is insufficient evidence to indicate that the average diameter of the tendon for patients with AT is greater than 5.97 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 5.97 mm.

Solutions

Expert Solution

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :   = 5.97

Ha : > 5.97

= 9.70

= 5.97

= 1.96

n = 31

= 5% = 0.05

Z = Z0.05 = 1.65

Z > 1.65

Test statistic = z = ( - ) / / n

= (9.70 - 5.97) / 1.96 / 31 = 10.60

Test statistic = 10.60

Test statistic > Critical value

H0 is rejected. There is sufficient evidence to indicate that the average diameter of the tendon for patients

with AT is greater than 5.97 mm.

milcah answered 2 months ago
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