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 2142 passenger cars in a particular region, 249 had only rear license plates. Among 332 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 0.10 significance level to test that hypothesis. 1. Test the claim using a hypothesis test. 2. 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. 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. ---------------(Round to two decimal places as needed.) Identify the P-value. ---------------(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. Fail to reject Ho. 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 Ho. 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. C. Fail to reject Ho. 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. D. Reject Ho. 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. b. Identify the confidence interval limits for the appropriate confidence interval. 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. ----------< p1 − p2 <-----------(Round to four decimal places as needed.) Because the confidence interval limits (1)----------- 0, there (2)--------- a significant difference between the two proportions. There (3)--------- 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. (1) contain do not contain (2) is is not (3) is not is

Answer 1

B. H0: p1 = p2 H1: p1 < p2

	passenger	Commerical drug
x=	249	49
n =	2142	332
p̂=x/n=	0.1162	0.1476
estimated prop. diff =p̂1-p̂2    =		-0.0313
pooled prop p̂ =(x1+x2)/(n1+n2)=		0.1205
std error Se=√(p̂1*(1-p̂1)*(1/n1+1/n2) =		0.0192
test stat z=(p̂1-p̂2)/Se =		-1.63
P value   =	0.0516	(from excel:1*normsdist(-1.63)

D. Reject Ho. 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.

b)

for 80 % CI value of z=		1.282	from excel:normsinv((1+0.8)/2)
margin of error E=z*std error =		0.026479
lower bound=(p̂1-p̂2)-E=		-0.0578
Upper bound=(p̂1-p̂2)+E=		-0.0049
from above 80% confidence interval for difference in population proportion =(-0.0578 <p1-p2<-0.0049)

1) do not contain   2) is 3) is