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 2083 passenger cars in a particular​ region, 230 had only rear license plates. Among 325 commercial​ trucks, 47 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 0.01 significance level to test that hypothesis.

a. Test the claim using a hypothesis test.

b. Test the claim by constructing an appropriate confidence interval.

a. 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.

A. Upper H 0 ​: p 1 equalsp 2Upper H 1 ​: p 1 less thanp 2 Your answer is correct.

B. Upper H 0 ​: p 1 equalsp 2Upper H 1 ​: p 1 greater thanp 2

C. Upper H 0 ​: p 1 equalsp 2Upper H 1 ​: p 1 not equalsp 2

D. Upper H 0 ​: p 1 less thanp 2Upper H 1 ​: p 1 equalsp 2

Identify the test statistic. nothing ​(Round to two decimal places as​ needed.)

Answer 1

Let population 1 correspond to the passenger cars and population 2 corresponds to the commercial trucks.

Let success be a vehicle that only has a rear license plate.

P1:- Proportion of vehicle that only has a rear license plate for passenger cars

P2:- Proportion of vehicle that only has a rear license plate for commercial trucks.

We want to test that commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars.

P1 < p2

The null & alternative hypothesis is

Ho: P1 =P2 vs Ha: P1 < P2