Please expalne how you got to the answer. In-store purchases. In 1999, the Ameri
ID: 3266441 • Letter: P
Question
Please expalne how you got to the answer.
In-store purchases. In 1999, the American Bankers Association reported rates of use as shown for different methods of payment for in store purchases. In a recent sample of 220 in-store purchases, 46 used credit card, 67 used debit card, 33 used personal check and 74 used cash. At alpha = 01, can we conclude that a change has occurred in how customers pay for in-store purchases? a) Give the appropriate null and alternative hypotheses b) Carry out the significance test for these data. Include the test statistic, degrees of freedom and the p-value. c) Give the conclusion in context.Explanation / Answer
a)
H0 : The proportion of credit card, debit card, personal check and cash is 46, 67 , 33 and 74,
respectively.
Ha : At least one of the proportions in the null hypothesis is false.
b)
df = k - 1 = 4 -1 = 3
Ei = n * pi = 220 * 0.25 = 55
E1 = 55 , E2 = 55 , E3 = 55 , E4 = 55
^2 = [ (Oi - Ei)2 / Ei ]
^2 = [ (46 - 55)^2 / 55 ] + [ (67 - 55)^2 / 55 ] + [ (33 - 55)^2 /55 + (74 - 55)^2/55 ]
^2 = 19.45
P value = 0.000221
The P-value is the probability that a chi-square statistic having 2 degrees of freedom is more extreme than 19.45
P(^2 > 19.45) = 0.000221.
c)
Since the P-value (0.000221) is less than the significance level (0.01), we cannot accept the null hypothesis.
Hence, we conclude that a change has occured in customers pay for in store purchases.