In a study examining smoking and lung cancer, a random sample of men between the ages of 55 and 60 was obtained. The smoking and disease status of each sampled subject was ascertained. For each subject, a ’1’ is assigned if the subject had lung cancer (case) and a ’0’ if not. Similarly, a ’1’ indicates that a subject is a smoker and a ’0’ indicates a nonsmoker. The data are found in the Excel file ‘LungCancer’.

• Read the data into R, and use table() function to produce a contingency table summa- rizing these data.

• Assuming that there is no association between smoking and lung cancer, compute a table of ‘expected’ counts.

• By hand, compute the observed value of the test statistic for testing association between lung cancer and smoking.

• Assuming there is no association, what is the distribution of the test statistic? • Using R, compute the p-value for a test of association, and give a detailed conclusion

based on the p-value and a comparison of the tables observed and expected counts.

2. The following data are from a study examining the incidence of tuberculosis in relation to blood groups in a sample of Eskimos. It is of interest to determine if there is any association between the disease and blood group within the ABO system.

Severity O A AB B Moderate-advanced 7 7 7 13

Minimal 27 34 12 18 Not Present 55 52 11 24

• Assuming that there is no association between disease and blood group, compute a table of ‘expected’ counts.

• By hand, compute the observed value of the test statistic for testing association between disease and blood group.

• Assuming there is no association, what is the distribution of the test statistic? • Using R, compute the p-value for a test of association, and give a detailed conclusion

based on the p-value and a comparison of the tables observed and expected counts.

3. The file ‘Anscombe’ contains 4 different datasets, each of which are based on a response Y, and a covariate X.Write the code in RStudio to solve the questions. Post all the codes in a document.