A company surveyed adult Americans about their consumer debt. The article reported that 48% of millennials (those born between 1980 and 1996) and 60% 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. USE SALT 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 H₂: P₁ P₂ > 0 O Ho: P₁ H₂: P₁ P₂ <0 P₂ > 0 O Ho: P₁ P₂ > 0 H₂: P₁-P₂ <0 O Ho: P₁ P₂0 H₂: P₁ P₂ <0 O Ho: P₁ P₂-0 H₂: P₁ P₂ *0 Find the test statistic. (Round your answer to two decimal places.)
A company surveyed adult Americans about their consumer debt. The article reported that 48% of millennials (those born between 1980 and 1996) and 60% 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. USE SALT 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 H₂: P₁ P₂ > 0 O Ho: P₁ H₂: P₁ P₂ <0 P₂ > 0 O Ho: P₁ P₂ > 0 H₂: P₁-P₂ <0 O Ho: P₁ P₂0 H₂: P₁ P₂ <0 O Ho: P₁ P₂-0 H₂: P₁ P₂ *0 Find the test statistic. (Round your answer to two decimal places.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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PLEASE ANSWER ALL THE PARTS OF THE QUESTION ( THIS IS NOT A GRADED ASSIGNMENT )
Transcribed Image Text:A company surveyed adult Americans about their consumer debt. The article reported that 48% of millennials (those born between 1980 and 1996) and 60% 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.
Ho: P₁
P₂ = 0
H₂: P₁
O Ho: P₁
H₂: P₁
O Ho: P₁
H₂: P₁
USE SALT
OH₁: P₁
Ha: P₁
O H₁: P₁
Ha: P₁
P₂ > 0
P₂ <0
P₂ > 0
P₂ > 0
P₂ <0
P₂ = 0
P₂ <0
P₂ = 0
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.
O We reject H. 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.
O We fail to reject Ho. 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.
O We reject H₂. 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.
O We fail to reject Ho. 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.
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