well as the final conclusion that addresses the original claim. Among 2106 passenger cars in a particular region, 225 had only rear license plates. Am 370 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 0.10 significance level to test that hypothesis. a. Test the claim using a hypothesis test. TI- PI-P Identify the test statistic. (Round to two decimal places as needed.)
well as the final conclusion that addresses the original claim. Among 2106 passenger cars in a particular region, 225 had only rear license plates. Am 370 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 0.10 significance level to test that hypothesis. a. Test the claim using a hypothesis test. TI- PI-P Identify the test statistic. (Round to two decimal places as needed.)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 30PPS
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identify the test statistics, p value, and confidence interval..
![**Hypothesis Testing of License Plate Violations**
**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.
**Data:**
- Among 370 commercial trucks, 56 had only rear license plates.
- Among 2106 passenger cars in a particular region, 225 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.
**Instructions:**
a. Test the claim using a hypothesis test.
**Hypotheses:**
- **Null Hypothesis (\(H_0\))**: \( p_1 \leq p_2 \)
- (The proportion of commercial trucks with only rear plates is less than or equal to the proportion of passenger cars with only rear plates.)
- **Alternative Hypothesis (\(H_1\))**: \( p_1 > p_2 \)
- (The proportion of commercial trucks with only rear plates is greater than the proportion of passenger cars with only rear plates.)
**Formula for Test Statistic:**
\[ Z = \frac{(\hat{p_1} - \hat{p_2}) - 0}{\sqrt{\hat{p}(1-\hat{p})(\frac{1}{n_1} + \frac{1}{n_2})}} \]
where:
- \(\hat{p_1} = \frac{x_1}{n_1}\) and \(\hat{p_2} = \frac{x_2}{n_2}\) are the sample proportions.
- \(\hat{p} = \frac{x_1 + x_2}{n_1 + n_2}\) is the pooled proportion.
**Identification of Test Statistic:**
\[ \hat{p_1} = \frac{56}{370} \]
\[ \hat{p_2} = \frac{225}{2106} \]
\[ \hat{p} = \frac{56 + 225}{370 + 2106} \]
**Steps to Complete:**
1. Calculate the sample proportions (\(\hat{p_1}\), \(\hat{p](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1bbe1ef9-cacf-48b7-b15f-bf536b5508cd%2Fa75b8314-99f4-40b2-b23d-b48b38741514%2Fadf57rd.jpeg&w=3840&q=75)
Transcribed Image Text:**Hypothesis Testing of License Plate Violations**
**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.
**Data:**
- Among 370 commercial trucks, 56 had only rear license plates.
- Among 2106 passenger cars in a particular region, 225 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.
**Instructions:**
a. Test the claim using a hypothesis test.
**Hypotheses:**
- **Null Hypothesis (\(H_0\))**: \( p_1 \leq p_2 \)
- (The proportion of commercial trucks with only rear plates is less than or equal to the proportion of passenger cars with only rear plates.)
- **Alternative Hypothesis (\(H_1\))**: \( p_1 > p_2 \)
- (The proportion of commercial trucks with only rear plates is greater than the proportion of passenger cars with only rear plates.)
**Formula for Test Statistic:**
\[ Z = \frac{(\hat{p_1} - \hat{p_2}) - 0}{\sqrt{\hat{p}(1-\hat{p})(\frac{1}{n_1} + \frac{1}{n_2})}} \]
where:
- \(\hat{p_1} = \frac{x_1}{n_1}\) and \(\hat{p_2} = \frac{x_2}{n_2}\) are the sample proportions.
- \(\hat{p} = \frac{x_1 + x_2}{n_1 + n_2}\) is the pooled proportion.
**Identification of Test Statistic:**
\[ \hat{p_1} = \frac{56}{370} \]
\[ \hat{p_2} = \frac{225}{2106} \]
\[ \hat{p} = \frac{56 + 225}{370 + 2106} \]
**Steps to Complete:**
1. Calculate the sample proportions (\(\hat{p_1}\), \(\hat{p
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