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 2148 passenger cars in a particular region, 231 had only rear license plates. Among 347 commercial trucks, 48 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.

Answer 1

a)

vs

We can use here,

  

=-1.69

P value is 0.0455 ........................by using NORMSDIST(-1.69)

P value is 0.0455 > 0.01

We fail to reject H0 at 0.01 level of significance .

We do not have sufficient evidence to say that,commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars.

b) We can use here , confidence interval formula

Z critical value at 0.01 level of significance is 2.58

=>(-0.0816,0.0200)

Above confidence interval contain 0 therefore, we fail to reject H0.