Question

X Instructor-created question Question Help Test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic P value and then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim Among 2079 passenger cars in a particular region 234 had only rear license plates Among 379 commercial trucks, 58 had only rear license plates. A reasonable hypothesis is that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars. Use a 0.05 significance level to test that hypothesis Identify the null and alternative hypotheses for this test Let population 1 correspond to the passenger cars and population 2 correspond to the commercial trucks Let a success be a vehicle that only has a rear license plate O A. Ho: PLP2 HP1 P2 OB. Ho-P1-P2 Hy Pu>P2 OCHOP:-P2 H₂ Pr #P2 OD. Ho PP H, P1-P2 Click to select your answers) and then click Check Answer 2 All parts showing Clea KA

Answer 1

The estimates of the sample proportios are ,

$\hat{p_1}=\frac{X_1}{n_1}=\frac{234}{2079}=0.1126$

$\hat{p_2}=\frac{X_2}{n_2}=\frac{58}{379}=0.1530$

The pooled estimate is ,

$\hat{P}=\frac{X_1+X_2}{n_1+n_2}=\frac{234+58}{2079+379}=0.1188$

The null and alternative hypothesis is ,

$H_0:p_1=p_2$

$H_a:p_1<p_2$

The test is left-tailed test.

The test statistic is ,

$Z_{stat}=\frac{\hat{p_1}-\hat{p_2}}{\sqrt{\hat{P}(1-\hat{P})(\frac{1}{n_1}+\frac{1}{n_2})}}=\frac{0.1126-0.1530}{\sqrt{0.1188(1-0.1188)(\frac{1}{2079}+\frac{1}{379})}}=-2.24$

The p-value is ,

p-value=$P(Z>|Z_{stat}|)=P(Z>2.24)=1-P(Z\leq 2.24)$

$=1-\Phi( 2.24)=1-0.9875=0.0125$ ; From standard normal distribution table

Decision : Here , p-value=0.0125<0.05

Therefore , reject Ho.

Conclusion : There is sufficient evidence to support the claim that the commercial truck owners violate laws requiring front license plates at a higher rate than owners of a passenger cars.