he given claim. Identify the null hypothesis, altenative 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 2126 passenger cars in a particular region, 228 had only rear license plates. Among 331 commercia trucks, 48 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. a. Test the claim using a hypothesis test. b. Test the claim by constructing an appropriate confidence interval. a. Identify the null and altermative 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. OA. Hạ: P:"P2 H: P

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**Hypothesis Testing: License Plate Law Compliance for Trucks and Cars**

**Problem Statement:**
Test the given claim by identifying the null hypothesis, alternative hypothesis, test statistic, and P-value. Conclude about the null hypothesis and address the original claim based on a significance level of 0.01. The hypothesis is that commercial trucks violate laws requiring front license plates at a higher rate than passenger cars.

**Sample Data:**
- Among 2126 passenger cars, 228 had only rear license plates.
- Among 331 commercial trucks, 48 had only rear license plates.

**Steps:**

**a. Null and Alternative Hypotheses:**
Identify hypotheses by defining Population 1 as passenger cars and Population 2 as commercial trucks.

- \( H_0: p_1 = p_2 \) 
- \( H_1: p_1 < p_2 \)

"Success" is defined as a vehicle having only a rear license plate.

**b. Test Statistic:**
Identify the test statistic.

- (Round to three decimal places as needed.)

**c. P-value:**
Identify the P-value.

- (Round to three decimal places as needed.)

**Conclusion on Null Hypothesis:**
State the conclusion concerning the null hypothesis and its implications for the original claim.

- **A.** Reject \( H_0 \): Support exists for the claim that trucks violate front license plate laws more than passenger cars.
- **B.** Reject \( H_0 \): Insufficient evidence to support the claim.
- **C.** Fail to reject \( H_0 \): Support exists for the claim.
- **D.** Fail to reject \( H_0 \): Insufficient evidence for the claim.

**d. Confidence Interval:**
Identify the confidence interval limits for comparison.

- \( p_1 - p_2 = \)
- (Round to four decimal places as needed.)

**Graphical Explanation:**
No graphs or diagrams are present in the text.
Transcribed Image Text:**Hypothesis Testing: License Plate Law Compliance for Trucks and Cars** **Problem Statement:** Test the given claim by identifying the null hypothesis, alternative hypothesis, test statistic, and P-value. Conclude about the null hypothesis and address the original claim based on a significance level of 0.01. The hypothesis is that commercial trucks violate laws requiring front license plates at a higher rate than passenger cars. **Sample Data:** - Among 2126 passenger cars, 228 had only rear license plates. - Among 331 commercial trucks, 48 had only rear license plates. **Steps:** **a. Null and Alternative Hypotheses:** Identify hypotheses by defining Population 1 as passenger cars and Population 2 as commercial trucks. - \( H_0: p_1 = p_2 \) - \( H_1: p_1 < p_2 \) "Success" is defined as a vehicle having only a rear license plate. **b. Test Statistic:** Identify the test statistic. - (Round to three decimal places as needed.) **c. P-value:** Identify the P-value. - (Round to three decimal places as needed.) **Conclusion on Null Hypothesis:** State the conclusion concerning the null hypothesis and its implications for the original claim. - **A.** Reject \( H_0 \): Support exists for the claim that trucks violate front license plate laws more than passenger cars. - **B.** Reject \( H_0 \): Insufficient evidence to support the claim. - **C.** Fail to reject \( H_0 \): Support exists for the claim. - **D.** Fail to reject \( H_0 \): Insufficient evidence for the claim. **d. Confidence Interval:** Identify the confidence interval limits for comparison. - \( p_1 - p_2 = \) - (Round to four decimal places as needed.) **Graphical Explanation:** No graphs or diagrams are present in the text.
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