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 2140 passenger cars in a particular region,246 had only rear license plates. Among 315 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 0.05 significance level to test that hypothesis.

a. Test the claim using a hypothesis test.

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

Answer 1

Ans:

a)

sample proportion for cars=246/2140=0.1150

sample proportion for trucks=45/315=0.1429

pooled proportion=(246+45)/(2140+315)=0.1185

Test statistic:

z=(01150-0.1429)/sqrt(0.1185*(1-0.1185)*((1/2140)+(1/315)))

z=-1.43

critical z value=-1.645

Fail to reject the null hypothesis.

There is not sufficient evidence to suggest that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars.

b)

95% confidence interval for difference in proportions

=(0.1150-0.1429)+/-1.96*sqrt((0.1150*(1-0.1150)/2140)+(0.1429*(1-0.1429)/315))

=-0.0279+/-0.0409

=(-0.0688, 0.0130)

As,above CI includes 0 within its limits,we can not conclude that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars.