Question

Q.6.2   The financial manager of a national warehouse chain has found from previous experience that 45% of clients pay by credit card, 35% pay on account, while the remainder pay using cash. He wishes to know if this is still the case. A random sample of 1000 sales receipts from the last month produced the following results: (8).

Payment Method
	Credit card	Account	Cash	Total
Number of receipts	500	315	185	1000

Using a 1% significance level, test whether the payment method pattern has changed.

Answer 1

observed frequencey, O	expected proportion	expected frequency,E			(O-E)²/E
500	0.450	450.00			5.556
315	0.350	350.00			3.500
185	0.200	200.00			1.125

Ho: two variables are independent of each other
H1: two variables are not not independent to each other

chi square test statistic,X² = Σ(O-E)²/E =   10.181              
                  
level of significance, α=   0.01              
Degree of freedom=k-1=   3   -   1   =   2
                  
P value =   0.0062   [ excel function: =chisq.dist.rt(test-stat,df) ]          
Decision: P value < α, Reject Ho                  

Hence the payment method pattern has changed.

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