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 2199 passenger cars in a particular​ region, 255 had only rear license plates. Among 354 commercial​ trucks, 49 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.

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. H0: ​p1=p2

    H1: p1>p2

B. H0​: p1=p2

H1​: p1≠p2

C. H0​: p1<p2

H1​: p1=p2

D. H0​: p1=p2

H1​: p1<p2

Identify the test statistic.

__

Identify the​ P-value.

__

State the conclusion about the null​ hypothesis, as well as the final conclusion that addresses the original claim.

A. Reject H0. There is not sufficient evidence to support the claim that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars.

B. Reject H0. There is sufficient evidence to support the claim that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars.

C. Fail to reject H0. There is not sufficient evidence to support the claim that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars.

D. Fail to reject H0. There is sufficient evidence to support the claim that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars.

Answer 1

The statistical software output for this problem is:

On the basis of above output:

Hypotheses: Option D is correct.

Test statistic = -1.21

P - value = 0.113

Conclusion: Option C is correct.