Question

A gambler is dealt the following observed distribution of suits in the course of 30 poker hands (5 cards each hand) with the same dealer. The gambler is convinced that the dealer is cheating. In a deck of cards, there are 13 cards of each of 4 suits, so the gambler expects close to equal amount of each suit. In this results table, the expected count appears below the observed count.

Clubs Diamonds Hearts Spades Total Observed 44 11 46 49 150 Expected 37.5 37.5 37.5 37.5 150

Which chi-square test is appropriate for this data (assuming the conditions are met)?

A. Goodness-of-fit

B. Test of homogeneity

C. Test of independence

Answer 1

We need to conduct the Chi-square goodness of fit test, based on a Uniform distribution of the variable.

Null Hyothesis, H0: The dealer is not cheating, hence dealing equal amount of each suit

Alternate Hyothesis, Ha: The dealer is cheating, hence not dealing equal amount of each suit

We can compute the expected frequencies as per below table. The Chi-square statistic has been computed using

Outcome	Observed	Expected	Chi-Square Statistic
Clubs	44	37.5	1.126666667
Diamonds	11	37.5	18.72666667
Hearts	46	37.5	1.926666667
Spades	49	37.5	3.526666667
Total	150	150	25.30666667

Critical Value: The test has 3 degrees of freedom, viz. one less than the number of categories. For 5% level of singificance, the critical value is

The observed statistic is in the critical range. That is, the test statistic 25.31 is less than the critical value 7.81. Hence, we must reject the null hypothesis and concude that the dealer is cheating, hence not dealing equal amount of each suit