Probability of observing mean difference/compute ranksum

#1
Hi everyone, would appreciate some help on these three questions. If possible with calculations so that I can understand more easily!

Suppose the endowment effect experiment were run with 5 people, 3 sellers and 2 buyers. Subjects arrive in the lab and pick numbers 1-5 out of the hat. If they get 1,2,3 they are a seller, if they get 4,5 they are a buyer. Sellers are given a mug and reveal their valuation by reporting their willingness to accept (WTA). Buyers reveal their valuation by reporting their willingness to pay (WTP). Suppose the WTA’s are 30, 25 and 20, while the WTPs are 2 and 4.

(a) What is exact probability of observing a mean difference in valuations this large or larger, if the treatment had no effect.

(b) What is exact probability of observing a median difference in valuations this large or larger, if the treatment had no effect.

(c) Compute the ranksum for the WTPs. What is exact probability of observing a ranksum this large or larger, if the treatment had no effect.

Thanks :)
 
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