Question

A company surveyed adult Americans about their consumer debt. They reported that 48% of Millennials (those born between 1980 and 1996) and 60% of Gen Xers (those born between 1965 and 1971) did not pay off their credit cards each month and therefore carried a balance from month to month. Suppose that these percentages were based on representative samples of 450 Millennials and 300 Gen Xers. Is there convincing evidence that the proportion of Gen Xers who do not pay off their credit cards each month is greater than this proportion for Millennials? Test the appropriate hypotheses using a significance level of 0.05. (Let P, be the proportion of Gen Xers who do not pay off their credit cards each month, and pz be the proportion of Millennials who do not pay off their credit cards each month.) L USE SALT State the appropriate null and alternative hypotheses. O Ho: P1 - P2 = 0 Hy: P - P20 Ho: P1 - P2 > 0 Ho: P2 - P2<0 O Ho: P2 - P2 - 0 Hy: P1-P2 > 0 O Ho: P2 - P2 - 0 Ho: P2 - P20 Ho: P.-P20 HP - P2 > 0 Find the test statistic and p-value. (Use a table or SALT. Round your test statistic to two decimal places and your p-value to four decimal places.) Z- p-value- State your conclusion. We fail to reject Ho. We have convincing evidence that the proportion of Gen Xers who do not pay off their credit cards each month is greater than this proportion for Millennials. We fail to reject Ho. We do not have convincing evidence that the proportion of Gen Xers who do not pay off their credit cards each month is greater than this proportion for Millennials. We reject Ho. We do not have convincing evidence that the proportion of Gen Xers who do not pay off their credit cards each month is greater than this proportion for Millennials. We reject Hy. We have convincing evidence that the proportion of Gen Xers who do not pay off their credit cards each month is greater than this proportion for Millennials.

Answer 1

Hypothesis can be formulated as: Ho: P.-P2 = 0 He : P.-P2>0 9+ is given theet, n = 300 P, = 0.60 P2 = 0.48 m = 450 Test Steelistic Z si - fPCP (Hit whese p=hip, thope nitha 180+ 216 300+450 396 150 = 0.528 Noco, Z - 0.6-0.48 10.528x0.472% ( + 450 - 0.12 = 3.2249986 0.0 372,093 3.2.2, P[273.22] = 0.000641 0.0006 Poralue = Here, p-value < a=0.05 Herco, we rejeet Ho. Therefore i loc conclude that love have convincing evidence that the proportion of Gen xess who do not pay off their Credit Cards each month is greater than this proportion of millenials,