Question

among 2049 passenger cars, 239 had only rear license plates. Among 334 trucks, 45 had only rear license plates. test the claim that passanger car owners violate license plate laws at a higher rate than owners of commercial trucks. use a 0.05 level of significance

Answer 1

Let sample 1 is sample of car passengers and sample 2 is sample of truck .

Let x denote owners that have rear license plates and y denotes owners who donot have rear license plates.

So we have : n1 = 2049, x1 = 239, y1 =1810, n2 = 334, x2 = 45, y2=289

Claim : Passanger car owners violate license plate laws at a higher rate than owners of commercial trucks.

This means owners who do not have rear lisense plate, violate laws.

Let is proportion of passengers that do not have rear license plates.

The hypothesis are :

H0 : P1 = P2 v/s H1: P1 > P2

The test statistic is,

Hence the test statistic value is,

= 0.521

Here we have = 0.05 , so the critical value is given by,

The calculated value of z < The critical value of z.

Hence we failed to reject H0.

Conclusion : There is no evidence to support the claim that passanger car owners violate license plate laws at a higher rate than owners of commercial trucks.