Do Angry People Have More Heart Disease? A study followed a random sample of 8474 people with normal blood pressure for about four years. All the individuals were free of heart disease at the beginning of the study. Each person took the Spielberger Trait Anger Scale test, which measures how prone a person is to sudden anger. Researchers also recorded whether each individual developed coronary heart disease (CHD). This includes people who had heart attacks and those who needed medical treatment for heart disease. Here is a two-way table that summarizes the data: (a) Calculate appropriate conditional distributions (in proportions) to describe the relationship between anger level and CHD status.

(b) Make a well-labeled graph that compares the conditional distributions in part (a). Do these data provide convincing evidence of an association between the variables in the larger population?

State: We want to perform a test of H0: There is no association between anger level and heart disease in the population of people with normal blood pressure. Ha: There is an association between anger level and heart disease in the population of people with normal blood pressure. Plan: If conditions are met, we should carry out a chi-square test of association/independence. Random: The data came from a random sample of 8474 people with normal blood pressure. Large Sample Size: all the expected counts are at least 5, so this condition is met. Independent : the total number of people in the population with normal blood pressure is at least 10(8474) = 84,740.

Do: We perform calculations assuming H0 is true. P- value : 0.00032 df=2 Conclude: Because the P-value is clearly less than α = 0.05, we have sufficient evidence to reject H0 and conclude that anger level and heart disease are associated in the population of people with normal blood pressure.

An advertising agency in a large city is conducting a survey of adults to investigate whether there is an association between highest level of educational achievement and primary source for news. The company takes a random sample of 2,500 adults in the city. The results are shown in the table below. (a) If an adult is to be selected at random from this sample, what is the probability that the selected adult is a college graduate or obtains news primarily from the internet? (b) If an adult who is a college graduate is to be selected at random from this sample, what is the probability that the selected adult obtains news primarily from the internet? 0.454 0.354

(c) When selecting an adult at random from the sample of 2,500 adults, are the events “is a college graduate” and “obtains news primarily from the internet” independent? Justify your answer. (d) The company wants to conduct a statistical test to investigate whether there is an association between educational achievement and primary source for news for adults in the city. What is the name of the statistical test that should be used? What are the appropriate degrees of freedom for this test? These events are not independent. Note that the unconditional probability P(obtains news primarily from the internet) = 0.275 but the conditional probability P(obtains news primarily from the internet /is a college graduate) = 0.354 Chi-square test of association (or independence), degrees of freedom = 8