A company surveyed adult Americans about their consumer debt. The article reported that 48% of millennials (those born between 1980 and 1996) and 62% 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

H_a: p₁ p₂ 0

H₀: p₁ p₂ > 0

H_a: p₁ p₂ < 0

H₀: p₁ p₂ < 0

H_a: p₁ p₂ > 0

H₀: p₁ p₂ = 0

H_a: p₁ p₂ < 0

H₀: p₁ p₂ = 0

H_a: p₁ p₂ > 0

Find the test statistic. (Round your answer to two decimal places.)

z =

Find the P-value. (Round your answer to four decimal places.)

P-value =

State your conclusion.

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 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 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.