Question

A company warveyed aduit Americans about the consumer debit. They reported that 15% of Millennials (the bombeban 1996) Chose born between 1965 and 1971) did not the crede cada each month and therefore carried a balance from manth to months that these percentage were based on represes of 450 Mills and 30 GenXurs. Is there convincing widence that the properties of an Xer who do not pay off their credit cards each month greater than the proportion for Millennials Test the hypotheses sin ince level of 0.05. (at the proportion of Geners who do not off the credit cards each month and the proportion of Millennials who do not pay their credit card ach month.) A USE SALT State the prorlate null and alternative hypotheses O HO M0 Mel PP HIPPO 9 Mo Pa- NPO С Но е? HP Find the best (use SALT. Hound you to topelto State Witte denne properti hard to We todo el techos the with the et vente Wej we do not withichewa

Answer 1

Here

For Gen Xers :

$\widehat{p}_{1}=0.59$

n₁ = 300

For Millennials :

$\widehat{p}_{2}=0.48$

n₂ = 450

The pooled sample proportion ($\widehat{p}$) is,

$\widehat{p}=\frac{\widehat{p}_{1}*n_{1}+\widehat{p}_{2}*n_{2}}{n_{1}+n_{2}}$

  $=\frac{0.59*300+0.48*450}{300+450}$

= 0.524

Now

Test statistic is,

$Z=\frac{\widehat{p}_{1}-\widehat{p}_{2}}{\sqrt{\widehat{p}(1-\widehat{p})\left ( \frac{1}{n_{1}}+\frac{1}{n_{2}} \right )}}$

$=\frac{0.59-0.48}{\sqrt{0.524(1-0.524)\left ( \frac{1}{300}+\frac{1}{450} \right )}}$

= 2.95502

  $\approx 2.96$

Since this is a one-tailed test, the p-value represents the probability that the z-score is greater than 2.96.

$P(Z>2.96) = 1-P(Z\leq 2.96)=1-0.9985=0.0015$

The P- value is 0.0015

Decision Rule :

Rejecting the null hypothesis when the P-value is less than the significance level.

Here

Significance level.= $\alpha$ = 0.05

Calculated P -value = 0.0015

Since p value is less than $\alpha$ , we reject H₀

We reject H_0, we have convincing evidence that the proportion of Gen Xers who do not pay off their credit cards each month is greater than the proportion for Millennials.