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 2082 passenger cars in a particular region, 224 had only rear license plates. Among 346 commercial trucks, 47 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 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. OA. Ho: P₁ P₂ H₁: P₁ P₂ OB. Ho: P₁ P₂ H₁: P₁ P₂ OC. Ho: P₁ P₂ H₁: P₁ P₂ OD. Ho: P₁ P₂ H₁: P₁ P₂ Identify the test statistic (Type an integer or a decimal. Round to two decimal places as needed.) Identify the P-value. (Type an integer or a decimal. Round to three decimal places as needed.) State the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Ho. There sufficient evidence to support the claim that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars. b. Identify the confidence interval limits for the appropriate confidence interval. 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.
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 2082 passenger cars in a particular region, 224 had only rear license plates. Among 346 commercial trucks, 47 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 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. OA. Ho: P₁ P₂ H₁: P₁ P₂ OB. Ho: P₁ P₂ H₁: P₁ P₂ OC. Ho: P₁ P₂ H₁: P₁ P₂ OD. Ho: P₁ P₂ H₁: P₁ P₂ Identify the test statistic (Type an integer or a decimal. Round to two decimal places as needed.) Identify the P-value. (Type an integer or a decimal. Round to three decimal places as needed.) State the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Ho. There sufficient evidence to support the claim that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars. b. Identify the confidence interval limits for the appropriate confidence interval. 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.
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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Transcribed Image Text:**Hypothesis Testing and Confidence Interval Analysis**
In this exercise, we are conducting a hypothesis test to determine if the rate at which owners of commercial trucks violate laws requiring front license plates is higher than that of passenger car owners. The information given includes:
- Among 2082 passenger cars, 224 had only rear license plates.
- Among 346 commercial trucks, 47 had only rear license plates.
- The significance level for the test is 0.01.
**a. Identifying the Null and Alternative Hypotheses**
- Let population 1 correspond to passenger cars and population 2 correspond to commercial trucks.
- A success is defined as a vehicle having only a rear license plate.
**Options for Hypotheses:**
- **A.** \( H_0: p_1 = p_2 \) and \( H_1: p_1 > p_2 \)
- **B.** \( H_0: p_1 < p_2 \) and \( H_1: p_1 = p_2 \)
- **C.** \( H_0: p_1 = p_2 \) and \( H_1: p_1 \neq p_2 \)
- **D.** \( H_0: p_1 = p_2 \) and \( H_1: p_1 < p_2 \)
**Test Statistic and P-value:**
- Identify and calculate the test statistic, then round to two decimal places.
- Identify and determine the P-value, rounding to three decimal places.
**Conclusion Step:**
- Decide whether to reject the null hypothesis (\( H_0 \)) or not based on the P-value and the significance level. Conclude whether there is sufficient evidence to support the claim regarding higher violation rates by commercial trucks.
**b. Confidence Interval Analysis**
- Calculate the confidence interval limits using an appropriate confidence level.
- Determine the interval for the difference between \( p_1 \) and \( p_2 \).
**Interpretation:**
- Use the confidence interval to assess the significance of the difference between the two proportions. Conclude whether there is sufficient evidence to support the claim regarding violation rates.
This exercise involves utilizing statistical methods to make informed conclusions based on sample data, offering valuable insights into real-world compliance behaviors.
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