n state the conclusion about the null hypothesis, as well as the final conclusion that es the original claim. Among 2077 passenger cars in a particular region, 240 had only ense plates. Among 304 commercial trucks, 44 had only rear license plates. A reasonable esis is that commercial trucks owners violate laws requiring front license plates at a ate than owners of passenger cars. Use a 0.01 significance level to test that hypothesis. che claim using a hypothesis test. the claim by constructing an appropriate confidence interval.

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### Hypothesis Testing and Statistical Analysis

**Objective:**  
Test the given claim about commercial trucks and passenger cars regarding rear license plates.

**Context:**  
- **Passenger Cars:** 2077 in total; 240 have only rear plates.
- **Commercial Trucks:** 304 in total; 44 have only rear plates.
- **Hypothesis:** Commercial trucks violate front license plate laws at a higher rate than passenger cars.
- **Significance Level:** 0.01

**Tasks:**  
a. Use a hypothesis test.  
b. Construct a confidence interval.

---

#### a. Identifying Hypotheses

**Null and Alternative Hypotheses Definitions:**

- **Population 1:** Passenger cars
- **Population 2:** Commercial trucks

The categorization of success is a vehicle having only a rear license plate.

**Options for Hypotheses:**

- **A.**  
  \( H_0: p_1 < p_2 \)  
  \( H_1: p_1 = p_2 \)

- **B.** (Selected as correct)  
  \( H_0: p_1 = p_2 \)  
  \( H_1: p_1 < p_2 \)

- **C.**  
  \( H_0: p_1 = p_2 \)  
  \( H_1: p_1 \neq p_2 \)

- **D.**  
  \( H_0: p_1 = p_2 \)  
  \( H_1: p_1 > p_2 \)

**Next Step:** Identify the test statistic.

- **Prompt:** Enter an integer or a decimal, rounded to two decimal places.  

This setup guides the hypothesis testing process, crucial for determining compliance with license plate laws.
Transcribed Image Text:### Hypothesis Testing and Statistical Analysis **Objective:** Test the given claim about commercial trucks and passenger cars regarding rear license plates. **Context:** - **Passenger Cars:** 2077 in total; 240 have only rear plates. - **Commercial Trucks:** 304 in total; 44 have only rear plates. - **Hypothesis:** Commercial trucks violate front license plate laws at a higher rate than passenger cars. - **Significance Level:** 0.01 **Tasks:** a. Use a hypothesis test. b. Construct a confidence interval. --- #### a. Identifying Hypotheses **Null and Alternative Hypotheses Definitions:** - **Population 1:** Passenger cars - **Population 2:** Commercial trucks The categorization of success is a vehicle having only a rear license plate. **Options for Hypotheses:** - **A.** \( H_0: p_1 < p_2 \) \( H_1: p_1 = p_2 \) - **B.** (Selected as correct) \( H_0: p_1 = p_2 \) \( H_1: p_1 < p_2 \) - **C.** \( H_0: p_1 = p_2 \) \( H_1: p_1 \neq p_2 \) - **D.** \( H_0: p_1 = p_2 \) \( H_1: p_1 > p_2 \) **Next Step:** Identify the test statistic. - **Prompt:** Enter an integer or a decimal, rounded to two decimal places. This setup guides the hypothesis testing process, crucial for determining compliance with license plate laws.
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