Question 1 (2 points) In April 2018, a cardiovascular study was carried out in the city of Framingham, Massachusetts (Source: https://www.kaggle.com/amanajmera1/framingham-heart- study-dataset/data). This long-term study collected data on 16 risk factors and ten- year risk of coronary heart disease. The nature of the risk factors presents an opportunity to employ the Chi square independence test to test the hypothesis of the association between the Ten-Year Risk of Coronary Heart Disease (TRCHD) and some risk factors. One of the risk factors measured is whether a participant had suffered stroke, participants respond "Yes" if they have had stroke and "No" if not. Please refer to the table below in answering the following questions. Disease Outcome Stroke (No) Stroke (Yes) Total TRCHD(No) 3086 13 3099 TRCHD(Yes) 549 8 557 Total 3635 21 3656 What are the null and alternative hypotheses for this problem Ho: Ten-year risk of coronary heart disease and stroke are correlated. HA: Ten-year risk of coronary heart disease and stroke are not correlated. Ho: Ten-year risk of coronary heart disease and stroke are independent. HA: Ten-year risk of coronary heart disease and stroke are dependent. Ho: Ten-year risk of coronary heart disease and stroke are related. HA: Ten-year risk of coronary heart disease and stroke are not related. Ho: Ten-year risk of coronary heart disease and stroke are associated. HA: Ten-year risk of coronary heart disease and stroke are not associated. Ho: Ten-year risk of coronary heart disease and stroke are positive. HA: Ten-year risk of coronary heart disease and stroke are negative. Question 2 (2 points) In April 2018, a cardiovascular study was carried out in the city of Framingham, Massachusetts (Source: https://www.kaggle.com/amanajmera1/framingham-heart- study-dataset/data). This long-term study collected data on 16 risk factors and ten- year risk of coronary heart disease. The nature of the risk factors presents an opportunity to employ the Chi square independence test to test the hypothesis of the association between the Ten-Year Risk of Coronary Heart Disease (TRCHD) and some risk factors. One of the risk factors measured is whether a participant had suffered stroke, participants respond "Yes" if they have had stroke and "No" if not. Please refer to the table below in answering the following questions. Disease Outcome Stroke (No) Stroke (Yes) Total TRCHD(No) 3086 13 3099 TRCHD(Yes) 549 8 557 Total 3635 21 3656 Calculate the expected values of the presence of a ten-year risk of coronary heart disease (TRCHD: NO) if the disease outcome and stroke are independent. O O O Stroke (No)= 1817.5, Stroke (Yes)= 10.5 O Stroke (No)= 1828, Stroke (Yes) = 1828 O Stroke (No)= 3081.199, Stroke (Yes)= 17.801 O Stroke (No)= 1949.502, Stroke (Yes)= 278.517 O Stroke (No)= 914, Stroke (Yes)= 914