A study of D. Kadell and D. Ylvisaker entitled “Lotto play: the good, the fair and the truly awful,” Chance Magazine 4 (1991): 22–25 analyzes the behavior of players in the lotto. They took 111,221,666 tickets that were manually filled in for a specific draw of the California Lotto 6/53 and counted how many combinations were filled in exactly k times for k = 0, 1,…, 20. In the table we give the observed values of the Nk, where Nk denotes the number of combinations filled in k times. Use a chi-square test to find out whether the picks chosen by the players are random or not.
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