A consumer preference experiment consists in having 40 randomly selected customers of a fast-food chain compare two di ent types (A and B, say) of...

A consumer preference experiment consists in having 40 randomly selected customers of afast-food chain compare two dient types (A and B, say) of ground beef patties. Let X bethe number of testers that prefer type A over type B. Let p be the unknown proportion ofpotential customers in the population who would prefer type A over type B. What is, con-ditionally on p, the distribution of X? The uncertainty about p is reflected in the researcherassigning to it a Beta distribution with parameters and .(a) What are the posterior mean and variance of p, after performing the experiment andobserving x testers preferring type-A patties?(b) Answer the previous question assuming that alpha = beta = 1/2 and 35 testers preferred type A