Question

1. It’s Friday night at the Tunisian Nights Casino, and renowned gambler Jeremy Turner is having a fantastic night at the blackjack table. Out of all of the 36 games played, he beats the dealer 28 times and loses to the dealer 8 times. You are convinced that he has been counting cards. The c² test can be used to estimate the likelihood that the number of wins Turner has had occurred by chance. Note: the total for both the observed and expected will be the total number of games he has played.

                       

Blackjack data

 = .05			Total
Observed
Expected

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

Interpret the results of the χ² analysis.

Answer 1

observed frequencey, O	expected proportion	expected frequency,E	(O-E)	(O-E)²	(O-E)²/E
28	0.500	18.00	10.00	100.00	5.556
8	0.500	18.00	-10.00	100.00	5.556

total = 36

Degree of freedom=k-1=   2   -   1   =   1
Critical value =    3.841
chi square test statistic,X² = Σ(O-E)²/E =   11.111
  
Significant= Y

there is enough evidence to conclude that  the number of wins Turner has had not occurred by chance