In a study investigating the effect of ultrasound therapy on

In a study investigating the effect of ultrasound therapy on knee extension, range of motion was measured in a sample of physical therapy patients before and after ultrasound treatment.

patient A B C D E F G

before 31 53 45 57 50 43 32

after 32 59 46 64 49 45 40

(a) Estimate the average difference between the before and after measurements, and give a 95% confidence interval for your estimate.

(b) Use either the paired-t test or the sign test to test the hypothesis Ha : µd > 0 at the = 0.05 level.

Solution

a) Estimate for difference: -3.43

b) using pair t test at level 0.05

N Mean StDev SE Mean
before   7 44.4 10.0 3.8
after    7 47.9 10.9 4.1

Difference = mu (C5) - mu (C6)
Estimate for difference: -3.43
95% upper bound for difference: 6.53
T-Test of difference = 0 (vs <): T-Value = -0.61 P-Value = 0.275 DF = 12
Both use Pooled StDev = 10.4506