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 2199 passenger cars in a particular? region, 238 had only rear license plates. Among 319 commercial? trucks, 43 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.

Identify the test statistic

Identify the p-value

Identify the confidence interval limits for the appropriate confidence interval. Let population 1 correspond to the passenger cars and population 2 correspond to the commercial trucks. Let a success be a vehicle that only has a rear license plate.

Answer 1

a) Here we are trying to test whether the commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars, therefore the null and the alternate hypothesis here would be given as:

b) The pooled proportion here is computed as:

Now the standard error here is computed as:

Now the test statistic here is computed as:

Therefore -1.4056 is the test statistic value here.

c) As this is a one tailed test, the p-value here is computed from the standard normal tables as:

p = P(Z < -1.4056 ) = 0.0799

Therefore 0.0799 is the required p-value here.

d) As we are doing the test on 0.05 level of significance, we get from the standard normal tables that:

P( -1.96 < Z <1.96 ) = 0.95

Therefore the confidence interval here is obtained as:

This is the required confidence interval here.