The American Bankers Association collects data on the use of credit cards, debit

Question

The American Bankers Association collects data on the use of credit cards, debit cards personal checks and cash when consumers pay for in store Purchases The Wall street Journal December 16, 2003). In 1999. the following usages were reported: A sample taken in 2003 found that for 210 in-store purchases. 36 used a credit card, 67 used a debit card, 33 used a personal 74 used a personal check, and 74 used cash. Fill in the observed and expected values. At a 0.01 significance level can we conclude that a change occurred in how customers paid for in- store purchases over the four-year period 1999 and 2003?

Explanation / Answer

Ans: Null hypothesis H0 :There is no significant change in how customers paid for in store purchases over the four year period.

Alternate hypothesis Ha :there is significant change in how customers paid for in store purchases over the four year period.

Expected count will be given by:

Credit card=210*0.22=46.2

Debit card=210*0.21=44.1

Personal Check=210*0.18=37.8

Cash=210*39=81.9

Calculated Chi square score=15.51

degree of freedom=4-1=3

p-value=0.00143

Significance level=0.01

As,p-value<0.01,We reject null hypothesis i.e. there is no significant change in how customers paid for in store purchases over the four year period.

Hence,it concludes that we have sufficient evidence that there is significant change in how customers paid for in store purchases over the four year period.

In store purchase Observed(O) Expected(E) (O-E)^2/E Credit card 36 46.2 2.25 Debit card 67 44.1 11.89 Personal Check 33 37.8 0.61 Cash 74 81.9 0.76 Total 210 210 15.51

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