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 2166 passenger cars in a particular region, 248 had only rear license plates. Among 375 commercial trucks, 55 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 0.10 significance level to test that hypothesis. a. Test the claim using a hypothesis test. b. Test the claim by constructing an appropriate confidence interval a. 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 vehicle that only has a rear license plate YA. Ho P1=P2

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 2166 passenger cars in a particular region, 248 had only rear license plates. Among 375 commercial trucks, 55 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 0.10 significance level to test that hypothesis. a. Test the claim using a hypothesis test. b. Test the claim by constructing an appropriate confidence interval a. 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 vehicle that only has a rear license plate YA. Ho P1=P2

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

9.1-1

**Hypothesis Testing and Confidence Interval Construction**

**Objective:**

To test the given claim, identify the null hypothesis, alternative hypothesis, test statistic, and P-value. Then, state the conclusion about the null hypothesis and provide the final conclusion that addresses the original claim.

**Problem Statement:**

Among 2166 passenger cars in a particular region, 248 had only rear license plates. Among 375 commercial trucks, 55 had only rear license plates. The hypothesis is that commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars. Use a 0.10 significance level to test this hypothesis.

**Tasks:**

a. Test the claim using a hypothesis test.

b. Test the claim by constructing an appropriate confidence interval.

**Part A: Hypothesis Testing**

1. **Identify the Null and Alternative Hypotheses:**
Let population 1 correspond to the passenger cars, and population 2 correspond to the commercial trucks. Define a "success" as a vehicle that only has a rear license plate.

- **Option A:**
- Null Hypothesis (\(H_0\)): \(p_1 = p_2\)
- Alternative Hypothesis (\(H_1\)): \(p_1 < p_2\)

- **Other options:**
- Option B: \(H_0: p_1 = p_2\); \(H_1: p_1 > p_2\)
- Option C: \(H_0: p_1 = p_2\); \(H_1: p_1 \neq p_2\)
- Option D: \(H_0: p_1 = p_2\); \(H_1: p_1 \neq p_2\)

The correct hypothesis for this problem is marked under Option A.

2. **Identify the Test Statistic:**

- Calculate the test statistic using the appropriate statistical test for comparing two proportions.

3. **Conclusion:**

According to the calculated test statistic and corresponding P-value (considering the 0.10 significance level), determine whether to reject the null hypothesis.

4. **Final Conclusion:**

Address the original claim based on the hypothesis test's results and state whether there is sufficient evidence that commercial truck owners violate the law requiring front license plates at a higher rate than passenger car owners.

(Note: For educational purposes, students are encouraged

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