Question

A company surveyed adult Americans about their consumer debt. They reported that 48% of Millennials (those born between 1980 and 1996) and 59% 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 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 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 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.

9.

Answer 1

Solution Gren? let P = The proportion of Gen xers pay off their credit cards each month. who do not do not pay P2= The proportion of Millennials who off their credit cards each month alternative hypothesis is the The null and 6 Ho: P, P2=0 titista tot adt 70 sulor ant H: P.-P270 Test statistics 15) lo PI = 0:59 Pa= 0.48 n2= 450 n = 300 Oes p = nifi traße 1 20 nitnzone = (0.59 *300 + (0.48*450) (750) 1 P = 0.524 Z= ✓ FCI-F) (1 h)

(0.59-0.48) Z- 0.5240)-0.524) Lu 3oot 450 5 adam Z=2.9550 o sind! 21 ind for wh Z=2.96 10 The value of the test statistic is 2.95 p-values pvalue = plzszo) painte =l-p(Z<zo) ) - PZ 2:34) -1- 0.99846 from table 20 0.0015 p-value = 0.001s P2.0) = Conclusion! 25 • We reject Ho. We have convincing evidence that the proportion of Gen Xers who do not pay off their credit cards credit cards each month is greater than this proportion for Millennials.