An investigator asked for the records of patients diagnosed with diabetes in his practice, then sampled 20 patients with cardiovascular disease (CVD) and 80 patients without CVD. For the sampled patients, he then recorded whether or not the age of onset of diabetes was at age 50 or younger. Of the 40 patients whose age of onset of diabetes was 50 years of age or earlier, 15 had cardiovascular disease. In the remaining 60 patients, 5 had cardiovascular disease.

(a) Write the contingency table that summarizes the result of this study.

(b) What is the relative odds of cardiovascular disease, comparing the older patients to those less than 50 years old at onset of diabetes?

(c) Interpret the relative odds of cardiovascular disease and comment on whether the relative odds cohere with what you might expect.

(d) In statistical terms, state the null hypothesis of no association between the presence of cardiovascular disease and age of onset of diabetes.

(e) What test can be used to test the null hypothesis? Are the assumptions for the test reasonably satisfied?

(f) The value of the chi-square test statistic for this table is 11. Identify the logical flaw in the following statement: "In this retrospective study of cardiovascular disease and diabetes, our study has demonstrated statistically significant evidence that diabetes increases the risk of cardiovascular disease."