Question

5.   Nine subjects, 87 to 96 years of age, were given 8 weeks of progressive resistance-weight training.
   Strength before and after the 8 weeks was measured for each individual by the maximum number
   of pounds that could be lifted. The results are shown below:

Before   3   3.5   4   6   7   8   8.5   12.5   15
After   7   17   19   12   19   22   28   20   28

   Find a 95% Confidence Interval for the strength gain.

Answer 1

Confidence interval for difference between two population means of paired samples is given as below:

Confidence interval = Dbar ± t*S_D/sqrt(n)

From given data, we have

Dbar = 11.61111111

S_d = 4.891176864

n = 9

df = n – 1 = 8

Confidence level = 95%

Critical t value = 2.3060

(by using t-table)

Confidence interval = 11.61111111 ± 2.3060*4.891176864/sqrt(9)

Confidence interval = 11.61111111 ± 2.3060*1.630392288

Confidence interval = 11.61111111 ± 3.7597

Lower limit = 11.61111111 - 3.7597 = 7.85

Upper limit = 11.61111111 + 3.7597 =15.37

7.85 pounds < µ_d < 15.37 pounds