Question

1. After Turner finishes at the Blackjack table, you (the casino’s statistician) follow him to a craps table. In two hours of playing, he's racked up $30,000 in winnings and is showing no sign of stopping. Crowds are gathering around him to watch his streak, and he is telling everyone within earshot that his good luck is due to the fact that he's using the casino's lucky pair of "bruiser dice," so named because one is black and the other blue. Unbeknownst to Turner, however, you have been quietly watching his rolls and marking down the values of each roll, noting the values of the black and blue dice separately. After 60 rolls, you have become convinced that the blue die is loaded: you’ve recorded the blue die rolling a one 16-times; a two 5-times; a three 9-times, a four 7-times; a five 6-times; and a six 17-times. The c² test can be used to estimate the likelihood that the values observed on the blue die occurred by chance.

Craps data

 = .05							Total
Observed
Expected

df = ______________   critical χ²= _________________      χ²= ___________________   Significant? Y or N

Interpret the results of the χ² analysis.

2. Based on the results of the χ² analyses, would you inform the owner of the casino of your discoveries and recommend Turner be thrown out? In other words, is Turner cheating? Why/why not?

Answer 1

category	observed frequencey, O	expected proportion	expected frequency,E	(O-E)	(O-E)²	(O-E)²/E
1	16	0.167	10.00	6.00	36.00	3.600
2	5	0.167	10.00	-5.00	25.00	2.500
3	9	0.167	10.00	-1.00	1.00	0.100
4	7	0.167	10.00	-3.00	9.00	0.900
5	6	0.167	10.00	-4.00	16.00	1.600
6	17	0.167	10.000	7.00	49.00	4.900

total = 60

level of significance, α=   0.05              
Degree of freedom=k-1=   6   -   1   =   5
Critical value =    11.070

chi square test statistic,X² = Σ(O-E)²/E =   13.600

significant : Y

there is enough evidence to conclude that  likelihood that the values observed on the blue die is not occurred by chance.