Question

A certain consumer research firm analyzed the 10​% of adults from a particular region that are either​ "Superbanked" or​ "Unbanked." Superbanked consumers are defined as adults who live in a household that has multiple asset accounts at financial​ institutions, as well as some additional​ investments; Unbanked consumers are adults who live in a household that does not use a bank or credit union. By finding the 5​% of adults that are​ Super banked, the firm identifies financially savvy consumers who might be open to diversifying their financial​ portfolios; by identifying the​ Unbanked, the firm provides insight into the ultimate prospective client for banks and financial institutions. As part of its​ analysis, the firm reported that 95​% of Super banked consumers from the region use credit cards in the past three months as compared to 36​% of Unbanked consumers. Suppose that these results were based on 1,000 Super banked consumers and 800 Unbanked consumers.

A. At the 0.1 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? State the null and alternative​ hypotheses, where π1 is the population proportion of Superbanked consumers that use credit cards and π2 is the population proportion of Unbanked consumers that use credit cards.

Determine the value of the test statistic.

ZSTAT=

Determine the critical​ value(s) for this test of hypothesis=

B. Find the​ p-value in​ (a) and interpret its meaning=

C. . Construct and interpret a 90%, 95% and 99​% confidence interval estimate for the difference between the Superbanked and the Unbanked with respect to the proportion that use credit cards.

Answer 1