You are told that a ball will be randomly drawn from one of two boxes (A and B), both of which contain black balls and red balls, and if a red ball is chosen, you will win $100. You are also told that Box A contains half black balls and half red balls, but you are not told the proportions in Box B. Which box would you pick?
a. Set up notation and specify hypotheses to test whether the population proportion who would pick Box A is 0.50.
b. For a random sample of 40 people, 36 pick Box A. Can you make a conclusion about whether the proportion for one option is higher in the population? Explain all steps of your reasoning. (Logically those who picked Box A would seem to think that Box B has greater chance of a black ball. However, a paradox first discussed by Daniel Ellsberg predicts that if they were now told that they would instead receive $100 if a black ball is chosen, they would overwhelmingly pick Box A again, because they prefer definite information over ambiguity.)