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. Suppose that a study is to be conducted to estimate the true mean of the diameter (in mm) of the affected Achilles tendon to within 1 mm. Assume the population standard deviation is 3.95mm. What sample size is required if

A. the level of confidence required is 95%?

B. the level of confidence required is 99%?

Answer 1

(A)Solution :

Given that,

E = 1

= 3.95

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

sample size n = (Z_/2* /En)²

=(1.96  * 3.95  / 1 )²

^{n = 60}

(b)Solution :

Given that,

E = 1

= 3.95

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

sample size n = (Z_/2* /En)²

=(2.576 *3.95  / 1 )²

^{n = 104}