Question

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 2126 passenger cars in a particular​ region, 237 had only rear license plates. Among 304 commercial​ trucks, 45 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 0.10 significance level to test that hypothesis.

Answer 1

H0: Null Hypothesis: P1 $\geq$ P2

HA: Alternative Hypothesis: P1 < P2

n1= 2126

p1 = 237/2126 = 0.1115

n2 = 45

p2 = 45/304 = 0.1480

nln2

= (237 + 45)/(2126 +304)

= 282/2430 = 0.1160

Q =1 - P =0.8840

SE = $\sqrt{PQ(1/n1+1/n2)}$

$=\sqrt{}$0.1160 X 0.8840 X (1/2126 + 1/304)

= 0.019634

Test statistic is:

Z = (0.1115 - 0.1480)/0.019634 = - 1.86

$\alpha$ = 0.10

From Table, critical value of Z = - 1.28

Since calculated value of Z = - 1.86 is less than critical value of Z= - 1.28, the difference is significant. Reject null hypothesis.

Conclusion:

The data support the claim that commercial truck owners violate laws at a higher rate than owners of passenger cars.