A study published in the the journal Public Library of Science took 134 people, who were at risk of a stroke, and divided them randomly into three groups. Group one had 36 people and they participated...

Extracted text: A study published in the the journal Public Library of Science took 134 people, who were at risk of a stroke, and divided them randomly into three groups. Group one had 36 people and they participated in a stress management program. Group two had 40 people and they took part in an exercise program, and the remaining people were in group three. People in group three were just monitored by their doctor. After three years the number in each group who had a stroke or a related condition were recorded. The results are as follows: group one had 19 stroke/related conditions; group two had 17 stroke/related conditions; and group three had 29 stroke/related conditions. Let pi be the population proportion of people at risk of a stroke participating in a stress management program having a stroke/related condition. Let p2 be the population proportion of people at risk of a stroke taking part in an exercise program having a stroke/related condition. Let p3 be the population proportion of people at risk of a stroke, who are just being monitored by a doctor having a stroke/related condition. Find the 95% confidence interval for p1 - Pzand give the lower bound. Give your answer to 3 decimal places.