Question: Exercises I and II presented data on grumpy old men and heart disease. In Chapter 4, the goal was to determine if there was a relationship between the two variables. A one tailed test may also make sense. We might hypothesize that if there is a difference in the probability of developing heart disease for men with no anger and men with lots of anger, the latter group would have a higher probability. Minitab output for testing this claim follows. Note that p1 is the probability of developing heart disease for men with no anger and p2 is the probability of developing heart disease for men with the most anger.
a. Write the null and alternative hypotheses in terms of p1 and p2, taking into account the claim being tested.
b. What is the value of the test statistic?
c. What conclusion would you reach using level of significance a = .01? Write your conclusion in statistical terms and in the context of the problem.
Exercises II: Exercise I concerned the relationship between anger and the risk of coronary heart disease. Some computer output for a chi-square test is shown below. What do the results indicate about the relationship? Explain.
Exercise I: Do grumpy old men have a greater risk of having coronary heart disease than men who aren't so grumpy? Harvard Medical School researchers examined this question in a prospective observational study reported in the November 1994 issue of Circulation (Kawachi et al., 1994). For 7 years, the researchers studied men between the ages of 46 and 90. All study participants completed a survey of anger symptoms at the beginning of the study period. Among 199 men who had no anger symptoms, there were 8 cases of coronary heart disease. Among 559 men who had the most anger symptoms, there were 59 cases of coronary heart disease.
a. Construct a contingency table for the relationship between degree of anger and the incidence of heart disease.
b. Among those with no anger symptoms, what percentage had coronary heart disease?
c. Among those with the most anger symptoms, what percentage had coronary heart disease?
d. Draw a bar graph of these data. Based on this graph, does there appear to be an association between anger and the risk of coronary heart disease? Explain.