Keywords: single sample proportion, comparing proportions
The Golden Casket is a long-standing Queensland lottery. Normally the Golden Casket sells 100,000 tickets. However the $2 Golden Casket No. 182, which was drawn at 10:10 am on 2 September 1998, sold an extra 10,000 tickets, making a total of 110,000 in all.
The results of the draw, published in the Courier Mail of 3 September 1998, show that a surprisingly large proportion of prizes had gone to the "extra" tickets, numbered 100,001 and above. The extra 10,000 tickets won 1133 out of the total 2363 tickets on offer:
|Prizes Won by Extra Tickets||Prizes Offered||Category of Prize|
|0||1||First Prize, $100,000|
|1||1||Second Prize, $1000|
|1||1||Third Prize, $500|
The following day the Golden Casket was forced to announce a redraw of Casket Draw 182. The Courier Mail of Saturday, 5 September 1998, reported
An anomaly in the numbers drawn for Casket Draw 182 has resulted in players being given a second chance to win next week and ensuring "all players are treated fairly".
However all of the winners from the original draw will still receive their prize money.
A Golden Casket spokesman said there may have been a possible technical hitch when the lottery was expanded from 100,000 to 110,000 tickets.
The spokesman said draw 182 was the first week of the expanded lottery and an unusually large amount of winning tickets were drawn in the 100,000 to 110,000 bracket.
The data is in the description above.
Mitchell Innes, news reporter for Channel 9 News, contacted Dr Gordon Smyth at the Department of Mathematics, University of Queensland, after the draw was published, to confirm that the results could not have occurred by chance. Dr Philip Pollett, of the Department of Mathematics, was also interviewed about the result, and appeared in a Channel 9 News item on Friday, 4 September.