Question 8, 9.1.18-T
HW Score: $31.39 \%, 6.28$ of 20 points
Points: 0 of 1
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 onginal claim. Among 2017 passenger cars in a particular region, 228 had only rear license plates. Among 318 commercial trucks, 44 had only rear license plates. A reasonable hyp amercial 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. est the claim using a hypothesis test.
Fest the claim by constructing an appropriate confidence interval.
Identify the null and alternative hypotheses for this test. Let population 1 correspond to the passenger cars and population 2 correspond to the commercial trucks. Let a success be a ly has a rear license plate.
A.
\[
\begin{array}{l}
H_{0}: P_{1}=p_{2} \\
H_{1}: P_{1}< P_{2}
\end{array}
\]
B.
\[
\begin{array}{l}
H_{0}: P_{1}=P_{2} \\
H_{1}: P_{1} \neq P_{2}
\end{array}
\]
c.
\[
\begin{array}{l}
H_{0}: P_{1}=P_{2} \\
H_{1}: P_{1}> P_{2}
\end{array}
\]
D.
\[
\begin{array}{l}
H_{0}: p_{1}< p_{2} \\
H_{1}-p_{1}=p_{2}
\end{array}
\]
Answer
Final Answer: \(\boxed{A}\)
Step 1 ：The question is asking to identify the null and alternative hypotheses for a test comparing the proportion of passenger cars and commercial trucks that only have rear license plates. The claim is that commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars.
Step 2 ：The null hypothesis is usually a statement of no effect or no difference. In this case, it would be that the proportion of passenger cars (P1) that only have rear license plates is equal to the proportion of commercial trucks (P2) that only have rear license plates.
Step 3 ：The alternative hypothesis is what we are testing against the null hypothesis. In this case, it would be that the proportion of commercial trucks (P2) that only have rear license plates is greater than the proportion of passenger cars (P1) that only have rear license plates.
Step 4 ：So, the null and alternative hypotheses should be: \[\begin{array}{l} H_{0}: P_{1}=P_{2} \\ H_{1}: P_{1} Step 5 ：This corresponds to option A in the question. Step 6 ：Final Answer: \(\boxed{A}\)
