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 conclusio addresses the original claim. Among 2086 passenger cars in a particular region, 243 had only rear license plates. Among 365 commercial trucks, 56 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 te 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 I vehicle that only has a rear license plate. O A. Ho P, = P2 H, P, #P2 O B. Ho P, =P2 H, P, P2 O D. Ho P,

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## Hypothesis Testing for License Plate Violations

### Scenario:
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 2086 passenger cars in a particular region, 243 had only rear license plates. Among 365 commercial trucks, 56 had only rear license plates. A reasonable hypothesis is that commercial truck 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.

### Steps to Follow:
#### a. Test the claim using a hypothesis test.
#### b. Test the claim by constructing an appropriate confidence interval.

### Identifying the Hypotheses:
#### a. Define 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.

- **Option A**:
  - H₀: p₁ = p₂
  - H₁: p₁ ≠ p₂

- **Option B**:
  - H₀: p₁ = p₂
  - H₁: p₁ < p₂

- **Option C**:
  - H₀: p₁ = p₂
  - H₁: p₁ > p₂

- **Option D**:
  - H₀: p₁ = p₁
  - H₁: p₁ ≠ p₂

**Select the Correct Hypotheses:**

After defining the hypotheses, identify the test statistic:
- Round to two decimal places as needed.

Please click to select your answer(s).
Transcribed Image Text:## Hypothesis Testing for License Plate Violations ### Scenario: 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 2086 passenger cars in a particular region, 243 had only rear license plates. Among 365 commercial trucks, 56 had only rear license plates. A reasonable hypothesis is that commercial truck 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. ### Steps to Follow: #### a. Test the claim using a hypothesis test. #### b. Test the claim by constructing an appropriate confidence interval. ### Identifying the Hypotheses: #### a. Define 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. - **Option A**: - H₀: p₁ = p₂ - H₁: p₁ ≠ p₂ - **Option B**: - H₀: p₁ = p₂ - H₁: p₁ < p₂ - **Option C**: - H₀: p₁ = p₂ - H₁: p₁ > p₂ - **Option D**: - H₀: p₁ = p₁ - H₁: p₁ ≠ p₂ **Select the Correct Hypotheses:** After defining the hypotheses, identify the test statistic: - Round to two decimal places as needed. Please click to select your answer(s).
**Testing a Claim About Violations of Front License Plate Laws**

When testing a claim, we follow these steps:

1. **Identify the null hypothesis, alternative hypothesis, test statistic, and P-value.**
2. **State the conclusion about the null hypothesis and provide the final conclusion that addresses the original claim.**

Let's consider a scenario involving commercial trucks and passenger cars. Specifically, we're testing the hypothesis that commercial truck owners violate laws requiring front license plates at a higher rate compared to owners of passenger cars. 

Here's the given data for the hypothesis test:

- **Passenger cars**: 
  - Population size = 2086 cars
  - Violations (only rear license plates) = 243
- **Commercial trucks**: 
  - Population size = 365 trucks
  - Violations (only rear license plates) = 56 
- **Significance level (α)**: 0.05

We perform two types of claims:
a. **Hypothesis Test**
b. **Confidence Interval**

**Part a: Hypothesis Test**

**Identify the P-value.** We need to determine whether we reject the null hypothesis (H₀):

- **Null Hypothesis (H₀)**: There is no significant difference in the violation rates between commercial trucks and passenger cars.
  
- **Alternative Hypothesis (H₁)**: The violation rate among commercial trucks is higher than that of passenger cars.

**Possible Conclusions:**
- **A.** Reject H₀. There is not sufficient evidence to support the claim that commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars.
- **B.** Fail to reject H₀. There is sufficient evidence to support the claim that commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars.
- **C.** Reject H₀. There is sufficient evidence to support the claim that commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars.
- **D.** Fail to reject H₀. There is not sufficient evidence to support the claim that commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars.

**Part b: Confidence Interval**

**Identify the confidence interval limits for the appropriate confidence interval.** Let population 1 correspond to passenger cars and population 2 correspond to commercial trucks. 

A "success" in this context means a
Transcribed Image Text:**Testing a Claim About Violations of Front License Plate Laws** When testing a claim, we follow these steps: 1. **Identify the null hypothesis, alternative hypothesis, test statistic, and P-value.** 2. **State the conclusion about the null hypothesis and provide the final conclusion that addresses the original claim.** Let's consider a scenario involving commercial trucks and passenger cars. Specifically, we're testing the hypothesis that commercial truck owners violate laws requiring front license plates at a higher rate compared to owners of passenger cars. Here's the given data for the hypothesis test: - **Passenger cars**: - Population size = 2086 cars - Violations (only rear license plates) = 243 - **Commercial trucks**: - Population size = 365 trucks - Violations (only rear license plates) = 56 - **Significance level (α)**: 0.05 We perform two types of claims: a. **Hypothesis Test** b. **Confidence Interval** **Part a: Hypothesis Test** **Identify the P-value.** We need to determine whether we reject the null hypothesis (H₀): - **Null Hypothesis (H₀)**: There is no significant difference in the violation rates between commercial trucks and passenger cars. - **Alternative Hypothesis (H₁)**: The violation rate among commercial trucks is higher than that of passenger cars. **Possible Conclusions:** - **A.** Reject H₀. There is not sufficient evidence to support the claim that commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars. - **B.** Fail to reject H₀. There is sufficient evidence to support the claim that commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars. - **C.** Reject H₀. There is sufficient evidence to support the claim that commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars. - **D.** Fail to reject H₀. There is not sufficient evidence to support the claim that commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars. **Part b: Confidence Interval** **Identify the confidence interval limits for the appropriate confidence interval.** Let population 1 correspond to passenger cars and population 2 correspond to commercial trucks. A "success" in this context means a
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