Question

A company surveyed adult Americans about their consumer debt. They reported that 46% of Millennials (those born between 1980 and 1996) and 60% of Gen Xers (these 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 Milenia? Test the hypotheses using a significance level of 0.05. (Let , be the proportion of Gen Xers who do not pay off their credit cards each month, and p, be the proportion of Millennials who do not pay of their propriate credit cards each month.) State the appropriatenus and alternative hypotheses Mo: P-P-0 MP - P<0 MOP, -P-0 MP - P2 > 0 Mo: P - PO M, P, -P, 0 Ho: Pg - P₂<0 MP - P >0 Hoip-P₂-0 H P -P -0 Find the test statistic and P.value(Use a table or technology. Round your test statistic to two decimal places and your value to four decimal places.) P-value - State your conclusion We reject 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 Milenia we fail to reject N. We have convincing evidence that the proportion of Geners who do not pay off their credit cards each month is greater than this proportion for Millennials we fail to reject. We do not have convincing evidence that the proportion of Geners who do not pay off their credit cards each month is greater than this proportion for Millennials. We reject H. 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 Milennials.

Answer 1

The statistical software output for this problem is:

Two sample proportion summary hypothesis test: P1 : proportion of successes for population 1 P2 : proportion of successes for population 2 P1-P2 : Difference in proportions Ho : P1 - P2 = 0 HA: P1 - P2 > 0 Hypothesis test results: Difference Counti Totali Count2 Total2 Sample Diff. Std. Err. Z-Stat P-value P1 - P2 180 300 207 450 0.14 0.037248714 3.7585191 <0.0001

Hence,

Hypotheses: Option B is correct.

z = 3.76

P-value = 0.0000

Conclusion: Option D is correct.