Question

A company surveyed adult Americans about their consumer debt. They reported that 46% 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 p1 be the proportion of Gen Xers who do not pay off their credit cards each month, and p2 be the proportion of Millennials who do not pay off their credit cards each month.) State the appropriate null and alternative hypotheses. H0: p1 − p2 > 0 Ha: p1 − p2 < 0 H0: p1 − p2 < 0 Ha: p1 − p2 > 0 H0: p1 − p2 = 0 Ha: p1 − p2 ≠ 0 H0: p1 − p2 = 0 Ha: p1 − p2 > 0 H0: 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 = State your conclusion. We fail to reject H0. 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 H0. 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 H0. 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 H0. 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

we have to test whether the proportion of Gen Xers who do not pay off their credit cards each month is greater than this proportion for Millennials

So, it is a right tailed hypothesis

H0: p1 − p2 = 0 Ha: p1 − p2 > 0

Using TI 84 calculator

press stat then test then 2-propZTest

enter the data

x1 = 0.61*300 = 183, n1 = 300, x2 = 0.46*450 = 207, n2 = 450

p1 > p2

press enter, we get

z statistic = 4.03

p value = 0.0001

it is clear that the p value is less than the significance level of 0.05, which means that the result is significant at 0.05 significance level

so, we will reject the null hypothesis

CONCLUSION:_ We reject H0. 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.