Question

A company surveyed adult Americans about their consumer debt. They reported that 47% of Millennials (those born between 1980 and 1996) and 61% 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 p, be the proportion of Millennials who do not pay off their credit cards each month.) State the appropriate null and alternative hypotheses. Ho: P1 P2 > 0 Ha: P1 P2 < 0 Ho: P1-P2<0 MA: P1-P2 > 0 Mo: P1-P2 = 0 Hy: P1 - P270 Mo: P1-P2 = 0 HP1-P20 Ho: P1 - P2 = 0 Ha: P1 P2 > 0 Find the test statistic and P-value. (Use a table or technology. Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value =

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 > p2

pcap = (X1 + X2)/(N1 + N2) = (183+212)/(300+450) = 0.5267

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.61-0.4711)/sqrt(0.5267*(1-0.5267)*(1/300 + 1/450))
z = 3.73

P-value Approach
P-value = 0.0001