Question: You are interested in the proportion of smokers. Consider a population consisting of N = 4 elements: the first two persons smoke, while the remaining two do not smoke. That is {S, S, N, N}
(a) In this population, what is the proportion of smokers?
(b) You take a random sample of size n = 2. How many different random samples are possible?
(c) Write down the sampling distribution of P, the sample proportion of smokers in a random sample of size n = 2 from this population. That is, list the possible outcomes (sample proportions of smokers) and the associated probabilities.
(d) Calculate the mean of the sampling distribution.