Question

According to the Heart and Stroke Foundation of Canada, in a recent year 17.6% of Canadians between the ages of 65 and 79 report having heart disease or stroke. Suppose you live in a province where the environment is conducive to good health and low stress and you believe these conditions promote healthy hearts. To investigate this theory, you conduct a random telephone survey of 20 persons 65 to 79 years of age in your province. a. On the basis of the figure from the Heart and Stroke Foundation, what is the expected number of people 65 to 79 years of age in your survey who have heart disease or stroke? b. Suppose only one person in your survey has heart disease or stroke. What is the probability of getting 1 or 0 people with heart disease or stroke in a sample of 20 if 17.6% of the population in this age bracket has this health problem? What do you conclude about your province from the sample data?

Answer 1

a) Expected number of people in your survey who have heart disease or stroke = n*p = 20*0.176 = 3.52

b) The number of persons having a heart disease follows a binomial distribution with p = 0.176 and n = 20

We need to find:

P(X=0) + P(X=1) = 20C0 * 0.176⁰ * 0.824²⁰ + 20C1 * 0.176¹ * 0.824¹⁹ = 0.1098

As the probability value of 0 or 1 people with heart disease or stroke in a sample of 20 is 0.1098, we do not have enough evidence to conclude that this is a significant result. If the p-value was less than 0.05, we could have said that this result is significant.