Question One (A) Asurvey, carried out at a major flower and gardening show, was concerned with the association between the intention to return to the show next year and the purchase of goods at this year’s show. There were 220 people interviewed and of these 101 had made a purchase; 69 of these people said they intended to return next year. Of the 119 who had not made a purchase; 68 said they intended to return next year. (i) Suppose one of the 220 people surveyed is selected at random. Calculate the probabilities of the selected persons; (a) Intends to return next year, given that he/she has made a purchase. [2 marks] (b) Intends to return next year, given that he/she has not made a purchase. [2 marks] (c) Has made a purchase, given that he/she intends to return next year. [2 marks] (ii) By testing the difference between the proportions of purchasers and nonpurchasers who intend to return next year, examine whether there is sufficient evidence concluding that the intention of return depends on whether or not a purchase was made. Interpret your results. [3 marks] (iii) Present the data as a contingency table and perform a χ2 (chi-square) test of association between the attributes ”intention to return” and ”purchasing status”. [4 marks] (iv) Discuss briefly the connection between the comparison of proportions carried out in part (ii) and the test of association performed in part (iii). [2 marks]
Probability and stats
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