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 20952095 passenger cars in a particular​ region, 239239 had only rear license plates. Among 400400 commercial​ trucks, 5757 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 0.100.10 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 carspassenger cars and population 2 correspond to the commercial truckscommercial trucks. Let a success be a vehicle that only has a rear license plate. A. Upper H 0H0​: p 1p1equals=p 2p2 Upper H 1H1​: p 1p1not equals≠p 2p2 B. Upper H 0H0​: p 1p1equals=p 2p2 Upper H 1H1​: p 1p1less than

p 2p2 Identify the test statistic. nothing ​(Round to two decimal places as​ needed.) Identify the​ P-value. nothing ​(Round to three decimal places as​ needed.) State the conclusion about the null​ hypothesis, as well as the final conclusion that addresses the original claim. A. RejectReject Upper H 0H0. There isis 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. Fail to rejectFail to reject Upper H 0H0. There isis 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 rejectFail to reject Upper H 0H0. There is notis 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. RejectReject Upper H 0H0. There is notis 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. Identify the confidence interval limits for the appropriate confidence interval. Let population 1 correspond to the passenger carspassenger cars and population 2 correspond to the commercial truckscommercial trucks. Let a success be a vehicle that only has a rear license plate. nothingless than

Answer 1

Test and CI for Two Proportions

Method

p₁: proportion where Sample 1 = passenger cars

p₂: proportion where Sample 2 = commercial trucks

Difference: p₁ - p₂

Descriptive Statistics

Sample	N	Event	Sample p
Sample 1	2095	239	0.114081
Sample 2	400	57	0.142500

Estimation for Difference

Difference	90% Upper Bound for Difference
-0.0284189	-0.004316

CI based on normal approximation

Test

Null hypothesis	H₀: p₁ = p₂
Alternative hypothesis	H₁: p₁ < p₂

Method	Z-Value	P-Value
Normal approximation	-1.51	0.0654

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Reject Ho