Solve b ### Hypothesis Testing and Confidence Interval ConstructionThis section demonstrates how to test a given claim using hypothesis testing and construct an appropriate confidence interval.#### Given Scenario:In a particular region, among 2022 passenger cars, 216 had only rear license plates. Among 385 commercial trucks, 52 had only rear license plates. The hypothesis is that commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars. A 0.10 significance level is used to test this hypothesis.### Part (a): Hypothesis Test**Step 1: Formulate Hypotheses**- Null Hypothesis \( (H_0) \): \( p_1 = p_2 \) (The proportion of violations is the same for both groups)- Alternative Hypothesis \( (H_1) \): \( p_1 \ne p_2 \) (The proportions of violations are different)**Step 2: Identify the Test Statistic**The test statistic calculated for this scenario is:\[ \text{Test Statistic} = -1.61 \](Rounded to two decimal places as needed)**Step 3: Identify the P-Value**The P-value is:\[ \text{P-value} = 0.054 \](Rounded to three decimal places as needed)**Step 4: State the Conclusion**Based on the P-value and the significance level:Since \( \text{P-value} < \text{Significance Level} \ ( \alpha = 0.10 ) \),\[ \boxed{\text{Reject } H_0. \text{ There is sufficient evidence to support the claim that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars.}} \]### Part (b): Constructing Confidence IntervalIdentifying the confidence interval limits:- Let \( \text{Population 1} \) correspond to the passenger cars.- Let \( \text{Population 2} \) correspond to the commercial trucks.- A success is defined as a vehicle that only has a rear license plate.The confidence interval for the proportion difference \( (p_1 - p_2) \) rounded to four decimal places is:\[ \boxed{-0.0961} \]This interval indicates that there is a statistically significant difference at this level of significance, hence supporting the initial alternative hypothesis.

(b) Obtain the 90% confidence interval for the difference between two proportions. The 90%…

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 2022 passenger cars in a particular region, 216 had only rear license plates. Among 385 commercial trucks, 52 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. OD. Ho: P₁ = P2 H₁: P₁ P₂ Identify the test statistic. -1.61 (Round to two decimal places as needed.) Identify the P-value. 054 (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. OA Fail to reject Ho. 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. B. Reject Ho. 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. OC. Fail to reject Ho. 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. OD. Reject Ho. There is not sufficient evidence 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.