Question

2.8 - PRP (platelet rich plasma) therapy is used to treat chronic joint pain and tendon injuries, using plasma derived from patients own blood. A recent study involving 230 patients with chronic joint or tendon pain reported that after receiving a PRP injection, 193 of them experienced at least a 25% reduction in pain.

a) Give a 95% confidence interval for the true proportion of patients with chronic joint or tendon conditions whose symptom are expected to be improved by PRP therapy, and interpret your interval.

b) Based on your confidence interval, comment on a treatment clinic’s claim that the treatment relieves pain in 85% of patients with such conditions.

(Show working out and formulas)

Answer 1

Solution:

Given:

Sample size= n = 230

x = Number of patients  experienced at least a 25% reduction in pain = 193

Part a) Give a 95% confidence interval for the true proportion of patients with chronic joint or tendon conditions whose symptom are expected to be improved by PRP therapy, and interpret your interval.

Formula:

where

and

We need to find z_c value for c=95% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.95) /2 = 1.95 / 2 = 0.9750

Look in z table for Area = 0.9750 or its closest area and find z value.

Area = 0.9750 corresponds to 1.9 and 0.06 , thus z critical value = 1.96

That is : Z_c = 1.96

Thus

Thus

Interpretation:

We are 95% confident that  true proportion of patients with chronic joint or tendon conditions whose symptom are expected to be improved by PRP therapy is between the limits:

Part b) Based on your confidence interval, comment on a treatment clinic’s claim that the treatment relieves pain in 85% of patients with such conditions.

Since confidence interval include claimed proportion = 0.85, thus there is sufficient evidence to support  a treatment clinic’s claim that the treatment relieves pain in 85% of patients with such conditions.