General Statistics Questions

1. A study looks at alcohol consumption in patients suffering from acute myocardial infarction (heart attacks). The patients were classified according to average number of alcoholic beverages per week, and whether or not they had congestive heart failure. A summary of the data is presented in the following table. (The Journal of the American Medical Association 2001) Alcohol consumption abstainers less than 7 drinks/week 7 or more drinks/week Heart failure yes 146 106 29 no 750 590 292 Conduct a two population proportions Z test to determine if alcohol consumption increases the chances of a heart attack. Conduct a Chi-square of independence to determine if heart failure and alcohol consumption are independent or not. Write a conclusion for each of the tests conducted. The results are similar or not? 2. Suppose that in a typical day the proportion of students that drive to campus is 30%, bike to campus is 40%, and the remaining 30% use some other way (walk, take a bus, get a ride). The campus sponsors a "Clear Air Day" to encourage people not to drive to campus. To evaluate if the campaign was a success, they wanted to determine if the proportions using each mode of transportation on that particular day differ from the norm. A random sample of 300 students was selected, and asked how they came to campus that day: Method Car Bike Other Count 80 125 95 State the null and alternate hypothesis Conduct the appropriate hypothesis test Write a conclusion in the context of the situation [NOTE: In SAS you have to order the data by "Method" alphabetically, otherwise SAS will do it for you automatically, and you will end up with the wrong answers.] BONUS QUESTION: Fisher's exact test can also be used to analyze 2 by 2 tables. Explain under which conditions you can use this test. What are the hypothesis for this test? Determine whether taking Echinacea reduces the risk of getting a cold by conducting (by hand) a Fisher exact test (data is shown below). Take Echinacea? Yes No Get a Yes 1 4 Cold? No 9 6