A survey asked subjects whether they believed in heaven and whether they believed in hell, and their responses are below.

1. (a)Test the hypothesis that the population proportions answering yes were identical for heaven and hell.
2. (b)Find a 95% confidence interval for the difference between the two population proportions.
3. (c)Estimate and interpret the odds ratio from a logistic model for the probability of a yes response as a function of the item (heaven or hell) using two different models: (i) A marginal model (ii) A subject specific model
4. (d)McNemar's test uses a normal approximation to the binomial distribution, but we need not make this approximation. We can use the binomial distribution directly and get exact p-values. Suppose I am interested in the following hypotheses: H0 :12 =21 v.s Ha :12 >21 Find an exact p-value to test these hypotheses