Question

1. Before the rush began for Christmas shopping, a department store had noted that the percentage of its customers who use the store's credit card, the percentage of those who use a major credit card, and the percentage of those who pay cash are the same. During the Christmas rush in a sample of 150 shoppers, 46 used the store's credit card; 43 used a major credit card; and 61 paid cash. With a = 0.05, test to see if the methods of payment have changed during the Christmas rush.

1. Fill in the table below

Payment method	Number of shoppers (observed)	Number of shoppers (expected)
Store credit card
Major Credit card
Cash
Total	150

2. Determine the degrees of freedom

3. Compute the test statistic

4. Perform the test to see if the methods of payment have changed

Answer 1

a)

	relative	observed	Expected
category	frequency(p)	Oi	Ei=total*p
Store credit card	1/3	46	50.00
Major credit card	1/3	43	50.00
Cash	1/3	61	50.00
total	1.000	150	150

b)

degree of freedom =categories-1=

2

c)

applying chi square goodness of fit test:

	relative	observed	Expected		Chi square
category	frequency(p)	Oi	Ei=total*p		R2i=(Oi-Ei)2/Ei
Store credit card	1/3	46	50.00		0.320
Major credit card	1/3	43	50.00		0.980
Cash	1/3	61	50.00		2.420
total	1.000	150	150		3.7200
test statistic X2 =		3.720

d)

for 0.05 level and 2 df :crtiical value X2 =

5.991

since test statistic does not falls in rejection region we fail to reject null hypothesis

we do not have have sufficient evidence to conclude that  methods of payment have changed