Historical customer transactions (or purchases) data for a major U.S. department store chain show the following proportions for the associated methods of payment:
Method of Payment Proportion of Transactions
Store Credit Card 0.31
Other Credit Card 0.21
Debit Card 0.23
Check 0.17
Cash ?
A random sample of 250 customer transactions shows the following methods of payment: store credit card = 75; other credit card = 57; debit card = 65; check = 39; cash = the rest. Can one infer, at α = 0.10, that the distribution of methods of payment for the transactions in the sample differs significantly from the historical distribution of methods of payment?
a. State the null and alternative hypotheses associated with the test.
b. What is the calculated value of the associated test statistic?
c. What is the critical value of the associated test statistic?
d. State your decision regarding the null hypothesis.
e. State your conclusion (meaning, describe what the decision means in this problem).