SHOW ALL WORK!

In a study of the risk factors for invasive cervical cancer that was conducted in Germany, the following data were collected relating smoking status to the presence or absence of cervical cancer.

Smoking status	cancer	No cancer	total
smoker	108	163	271
nonsmoker	117	268	386
total	225	431	656

(a) Calculate all joint, marginal, and conditional probabilities of the above table. Show the sum of all joint probabilities equals 1. Similarly show the sum of the marginal probabilities equals 1.

(b) Estimate the relative risk and its 95% CI of invasive cervical cancer for smokers relative non-smokers. Interpret your result.

(c) Estimate the odds ratio and its 95% CI of invasive cervical cancer for smokers relative non-smokers. Interpret your results.

(d) Show = (12) mathematically and using the (11) 22 cancer data presented in the table, where 1 = the probability of cancer among smokers and 2 = the probability of cancer among nonsmokers.