Question

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5. A small art gallery in Laguna Beach has the choice of stocking eisher oil paintings or finger paintings for a given tourist season. The oil paintings require a substantial investment, but the potential returns ae also greater. The return (profit or loss) depends on whether or not the tourists that season are primarily serious art collectors or more buyers. A sales analysis gives the following expectation. Season return ($1000) Stock decision Oil paintings Finger paintings Type of tourists Art collectors Casual buyers 135 -5 25 Let p be the probability that the type of tourist is primarily art collectors, so (1-p) is the probability of primarily casual buyers. (a) As a function of p. what is the expected return for stocking oil painting As a function of p, what is the expected return for stocking finger paintings? (b) what does it mean in context for p to be greater or less than chis value? (e) For what value of p are the two expected returns the same, and regions, 33 out of 150 reported seasons with tourists who were primarily art collectors. Construct a 95% confidence interval for the proportion of similar establishments with tourists who were (d) In a random sample of similar establishments in similar tourist art collectors. (e) Use the above resuls to justify a decision to stock finger paintings.

Answer 1

la) (135 135b-35 +35 5b + 25 -25 170ト-35 ー-30 +25 20 b= 35+25 tc) = 33 =0.22 95% C,D. = 0.22 ± o.066