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 2197 passenger cars in a
particular? region, 256 had only rear license plates. Among 346
commercial? trucks, 53 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.

Identify the test statistic:

Identify the p-value

Identify the confidence interval limits

Answer #1

Null Hypothesis H0: P1- P2 =

Alternative Hypothesis H1: P1 - P2 < 0

For owners of pasenger cars , the proportion is p1 = 256/2197= 0.1165

For Commercial truck owners , the proportion is p2 = 53/346 =0.1532

Under H0, the test statistic is

where

The critical value of Z at 1% significance level is -2.33

The P-Value is 0.0261

Level of significance = 0.01

Since p value is greater than significance level, Fail to Reject H0.

Hence, we donot enough evidence to support the claim that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars

99% Confidence Interval

Answer: -0.0897<(p1-p2)< 0.0163

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