Consumer research firm Scarborough analyzed the 10% of American adults who are either "Super-banked" or "Unbanked." Super-banked consumers are defined as U.S. adults who live in a household that has multiple asset accounts at financial institutions, as well as some additional investments; Unbanked consumers are U.S. adults who live in a household that does not use a bank or credit union. By finding the 5% of Americans who are Superbanked, Scarborough identifies financially savvy consumers who might be open to diversifying their financial portfolios; by identifying the Unbanked, Scarborough provides insight into the ultimate prospective client for banks and financial institutions. As part of its analysis, Scarborough reported that 93% of Superbanked consumers use credit cards as compared to 23% of Unbanked consumers. (Data extracted from bit.ly/Syi9kN.) Suppose that these results were based on 1,000 Superbanked consumers and 1,000 Unbanked consumers.
a. At the 0.01 level of significance, is there evidence of a significant difference between the Superbanked and the Unbanked with respect to the proportion that use credit cards?
b. Determine the p-value in (a) and interpret is meaning.
c. Compare the results of (a) and (b) to those of Problem 10.32 on page 368.