Question

You want to see if a card dealer is favoring one suit over another. You observe the dealer pick a card, put it back in the deck, shuffle, and then repeat the process 280 times. The results are displayed in the table below. Use an a = 0.01 significance level. a. Complete the rest of the table by filling in the expected frequencies: Frequencies of Suits Dealt Outcome Frequency Expected Frequency Spades 85 Hearts 61 Diamonds 67 Clubs 67 b. What is the correct statistical test to use? Select an answer c. What are the null and alternative hypotheses? HO: The distribution of suits is uniform. The distribution of suits is not uniform. The suits and cards are independent. The suits and cards are dependent. H: The distribution of suits is not uniform. The suits and cards are dependent. The distribution of suits is uniform. The suits and cards are independent. d. The degrees of freedom - e. The test-statistic for this data = (Please show your answer to three decimal places.)

Answer 1

(a)

Here n=4 0 E =(20)/n = 280/4 (0-E) (0-E)?/E 85 70 15 3.2143 61 70 -9 1.1571 67 70 -3 0.1286 67 70 -3 0.1286 Total 280 280 4.629

(b) Chi square goodness of fit

(c)  

Ho :

The distribution of suits is uniform.

H1 :  

The distribution of suits is not uniform.

(d)  

Degrees of freedom = 4-1 = 3

(e)

The test statistic is x2 = (0-E)? E 4.629

(f)

P-value = 0.2011 [using Excel function CHIDIST(4.629,3)]

(f) Ans : greater than

(g) fail to reject H0

(i)

There is insufficient evidence to conclude that the distribution of suits is not uniform.