Your assignment is to prepare and submit a paper on does smoking cause lung cancer. It is much easier to consider the problem from an epidemiological point of view. It is enough to prove that the risk of developing lung cancer in the population of smokers is significantly higher than that in the population of non-smokers. In this respect, we need to define the population of smokers. Naturally, an effect of smoking in the population who have been smoking more than a pack of cigarettes for the last 20 years is much more than the effect of smoking in a population who smoke at most 3 cigarettes a day for last five years. The probability of developing lung cancer is expected to be more in the former group than in the latter. Let us consider the population of longtime smokers. e.g. the population consists of males or females who have been smoking more than a pack of cigarettes for the last 20 years or more.
Let π1 be the probability of developing lung cancer in the group of smokers and let π2 be the probability of developing lung cancer in the group of non-smokers. Test the null hypothesis of equality of the two proportions versus the alternative that π1 >. π2. Mathematically, we may write
Equivalently we may say that under the null hypothesis the odds of developing lung cancer in the population of smokers is 1 against the alternative that the odds are greater than 1. Let the odds of developing lung cancer be denoted by θ. Hence, the equivalent hypothesis is
To test the above null hypothesis data need to be collected from a sample of smokers and another sample of non-smokers. Recall that we have defined the smoker population as who have been smoking more than one pack of cigarettes for past 20 years or so. Those who had smoked for more than 20 years but are current non-smokers are not included in the study. Ordinarily, such hypotheses may be tested by collecting data from a cross-section of the .population. However, lung cancer is a rare disease and to have a good enough representation of deceased persons in the sample a retrospective study is recommended.