K 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 2073 passenger cars in a particular region, 222 had only rear license plates. Among 339 commercial trucks, 51 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. OA. Ho: P₁ = P2 H₁: P₁ P2 OB. Ho: P1 P2 H₁: P₁ P2 OC. Ho: P₁ H₁: P₁ OD. Ho: P₁ P2 P2 P2 H₁: P₁ P2 Identify the test statistic. (Round to two decimal places as needed.). Identify the P-value. (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. Reiert He. There is 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.
K 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 2073 passenger cars in a particular region, 222 had only rear license plates. Among 339 commercial trucks, 51 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. OA. Ho: P₁ = P2 H₁: P₁ P2 OB. Ho: P1 P2 H₁: P₁ P2 OC. Ho: P₁ H₁: P₁ OD. Ho: P₁ P2 P2 P2 H₁: P₁ P2 Identify the test statistic. (Round to two decimal places as needed.). Identify the P-value. (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. Reiert He. There is 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.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.CR: Chapter 12 Review
Problem 16CR
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Transcribed Image Text:### Hypothesis Testing: License Plate Law Violations Among Vehicles
#### Problem Statement:
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.
**Context:**
Among 2073 passenger cars in a particular region, 222 had only rear license plates. Among 339 commercial trucks, 51 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.
You can test this claim by:
a. Using a hypothesis test.
b. Constructing an appropriate confidence interval.
#### a. Identifying the Hypotheses:
- **Null Hypothesis (H₀):** The proportion of passenger cars with only rear license plates is equal to the proportion of commercial trucks with only rear license plates.
- **Alternative Hypothesis (H₁):** The proportion of passenger cars with only rear license plates is less than the proportion of commercial trucks with only rear license plates.
Select the correct hypotheses from the options:
A. \( H_0: p_1 = p_2 \)
\( H_1: p_1 > p_2 \)
B. \( H_0: p_1 = p_2 \)
\( H_1: p_1 < p_2 \)
C. \( H_0: p_1 = p_2 \)
\( H_1: p_1 \ne p_2 \)
D. \( H_0: p_1 < p_2 \)
\( H_1: p_1 = p_2 \)
(Select the correct hypothesis by checking the appropriate box.)
#### b. Calculation Steps:
1. **Identify the test statistic:**
(Round to two decimal places as needed.)
2. **Identify the P-value:**
(Round to three decimal places as needed.)
#### Conclusion:
- **State the conclusion about the null hypothesis:**
- Reject \( H_0 \)
- Do not reject \( H_0 \)
(Select the correct option by checking the appropriate box.)
- **Final conclusion:**
- There is sufficient evidence to support the claim that commercial trucks owners violate laws requiring front license plates at a higher rate than
![### Hypothesis Testing for License Plates Compliance
**Problem Statement:**
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 2073 passenger cars in a particular region, 222 had only rear license plates. Among 339 commercial trucks, 51 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 0.10 significance level to test that hypothesis.
1. **Formulate the Hypotheses:**
- **Null Hypothesis (H₀):** There is no difference in violation rates of front license plates between commercial trucks and passenger cars.
- **Alternative Hypothesis (H₁):** Commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars.
2. **Testing the Claim using a Hypothesis Test:**
*Identify the test statistic.*
- [ ] (Round to two decimal places as needed.)
*Identify the P-value.*
- [ ] (Round to three decimal places as needed.)
3. **Conclusion Regarding Hypotheses:**
*State the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim.*
- [ ] A. Reject H₀. There is 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. Fail to reject H₀. There is 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.
- [ ] C. Reject H₀. There is not 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.
- [ ] D. Fail to reject H₀. There is not 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.
4. **Testing the Claim using a Confidence Interval:**
*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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5cc7f00e-28f4-4f9d-9775-3cbc7937b5d3%2F99a87127-8c6a-4ad5-8c99-01f64c187906%2Fxavyrbc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing for License Plates Compliance
**Problem Statement:**
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 2073 passenger cars in a particular region, 222 had only rear license plates. Among 339 commercial trucks, 51 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 0.10 significance level to test that hypothesis.
1. **Formulate the Hypotheses:**
- **Null Hypothesis (H₀):** There is no difference in violation rates of front license plates between commercial trucks and passenger cars.
- **Alternative Hypothesis (H₁):** Commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars.
2. **Testing the Claim using a Hypothesis Test:**
*Identify the test statistic.*
- [ ] (Round to two decimal places as needed.)
*Identify the P-value.*
- [ ] (Round to three decimal places as needed.)
3. **Conclusion Regarding Hypotheses:**
*State the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim.*
- [ ] A. Reject H₀. There is 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. Fail to reject H₀. There is 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.
- [ ] C. Reject H₀. There is not 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.
- [ ] D. Fail to reject H₀. There is not 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.
4. **Testing the Claim using a Confidence Interval:**
*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
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