The American Bankers Association collects data on the use of cards, personal che

Question

The American Bankers Association collects data on the use of cards, personal checks, and cash when consumers pay for in-store purchase. In usages were reported. a = 0.05. A sample taken in 2003 found that for 100 in-store purchases, 36 used a debit card, 23 used a personal check, and 24 used cash. The researchers are a change occurred in how customers paid for in-store purchase. (a) State the null hypothesis and alternative hypothesis. (b) Compute the test statistic. (c) What is the critical value? What is your conclusion for this test?

Explanation / Answer

a)

H0: The customers paid for in-store purchase are consistent with a specified distribution.

Ha: The customers paid for in-store purchase are not consistent with a specified distribution.

b) Consider the following table:

Test statistic, ²= (O-E)²/E = 16.829

c) df=k-1=4-1=3

Critical value at =0.05, is 7.815.

Since ² = 16.829 > 7.815, reject null hypothesis. There is sufficient evidence to conclude that the customers paid for in-store purchase has changed.

In-Store purchase Percentage(p) O E=N*p (O-E)²/E Credit Card 22% 36 22 8.909 Debit Card 21% 17 21 0.762 Personal check 18% 23 18 1.389 Cash 39% 24 39 5.769 Total 1 N=100 100 16.829

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