Question

Before the Christmas shopping rush began, a department store had noted that the percentage of customers who use a major credit card, the percentage who use the store’s credit card, the percentage who pay by debit card, and the percentage who pay with cash are all the same, 25% for each. During the Christmas season, in a sample of 200 shoppers, 68 used a major credit card, 42 used the store’s credit card, 45 paid with cash, and 45 paid with a debit card. At a 95% confidence level, test to see if the methods of payment have changed during the Christmas shopping rush.

Answer 1

null hypothesis:Ho:  methods of payment is same  during the Christmas shopping rush as earlier.

Alternate hypothesis:Ha:  methods of payment has changed during the Christmas shopping rush as earlier.

degree of freedom =categories-1=

3

for 0.05 level and 3 degree of freedom :rejection region =

7.815

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
major credit card	0.25	68	50.00	2.55	6.480
credit card	0.25	42	50.00	-1.13	1.280
cash	0.25	45	50.00	-0.71	0.500
debit card	0.25	45	50.00	-0.71	0.500
total	1.000	200	200		8.760

here as test statistic 8.760 is higher than critical value we reject null hypothesis

we have sufficient evidence at 0.05 level to conclude that  methods of payment have changed during the Christmas shopping rush