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 2031 passenger cars in a particular​ region, 227 had only rear license plates. Among 300 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 0.01 significance level to test that hypothesis.

a. Identify the null and alternative hypotheses for this test. Let population 1 correspond to the and population 2 correspond to the commercial trucks . Let a success be a vehicle that only has a rear license plate. 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.

b. Identify the confidence interval limits for the appropriate confidence interval. Let population 1 correspond to the and population 2 correspond to the . Let a success be a vehicle that only has a rear license plate. Because the confidence interval limits does/do not contain ​0, there is a significant difference between the two proportions. There is sufficient/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.

Answer 1

227 = 011 7 let Pi - 2 Þz = 203) YC0:15 300 -) Ho: P = P2 th: P L P₂ Z PR PAC ++) test StatestC: = 0.12 where pe htl2 nitna 227+45 203)+300 Qul-p:0.88 o.1 -0.15 Z? -1.99 No1210.38) (2 031417000 10.0233) [from 2-4able) + p-value ret los be ve0.0) 7 since, p-value >0.01, donot reject to ... we can'tconclude that, the commercial trucks owners Violate laws requering front license plates at a higher rate than owners of passenger cams.

a) let los be 0.01 Zoop= 2.576 (from 7 - table) 99:1-(I: 1p-pl) 1 z 1,01-10), 8(-k) MA PA BO DO 10.11-0'15) 19.576 0.11C1-0.113 + 203) 0.1511-0.15 300 -0.04 + 0.044 (0.084, 0.004) Since the confrdence of val [imats does contains 0, there as not sufficient evidence to support the that the clafon Commercial truck Owneus Vrolates front license laws requering plates at a higher rate than a owners of passenger COIS.