Question

Among 21802180 passenger cars in a particular​ region, 246246 had only rear license plates. Among 302302 commercial​ trucks, 4444 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 0.100.10 significance level to test that hypothesis.

Answer 1

There is statistical evidence at 1% significance level to support that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars.

Explanation:

Given that among 2180 passenger cars in a particular​ region, 246 had only rear license plates. Among 302 commercial​ trucks, 44 had only rear license plates.

Cars Trucks Total

Total 2180 302 2482

X 246 44 290

p 0.1128 0.1457 0.1168

`H_0:  p_1  = p_2\\H_a:   p_1 <p_2\\`

(left tailed test at 1% significance level)

Std error of p =
`\sqrt{(0.1168*0.8832)/(2482) } \\=0.0064`

Test statistic Z = p differnce/std error =

`(0.1128-0.1457)/(0.0064) \\\\=-5.14`

p value <0.0001

Since p is less than 1% we reject null hypothesis

There is statistical evidence at 1% significance level to support that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars.