Smoking. An insurance company would like to offer discounts on its life-insurance policies to nonsmokers. In a study, they asked 200 randomly selected men who are 60 years old whether they smoke at least one pack of cigarettes per day and if they have ever suffered from heart disease.

In the sample, 56 people were smokers, and, of those, 21 people have suffered from a heart disease. Of the 144 nonsmokers, 28 people have suffered from a heart disease.

a) Is there evidence that the percentage of people suffering heart disease is different in the two groups?

b) Give a 95% confidence interval for the difference in proportions.