### Understanding Hypothesis Testing in Automotive SafetyAn insurance actuary claims that the mean footwell intrusions for small and midsize cars are equal. Crash tests at 35 mph were conducted on 9 small cars and 6 midsize cars. The footwell intrusion for each car type was measured, focusing on the driver's legs. Here are the results:- **Small Cars**: Mean footwell intrusion = 7.8 centimeters, Standard deviation = 3.97 centimeters- **Midsize Cars**: Mean footwell intrusion = 11.9 centimeters, Standard deviation = 4.02 centimetersAt a significance level (α) of 0.05, use the following steps to determine the validity of the actuary's claim.#### Task 1: Identify the Claim and Formulate Hypotheses- **Correct Claim Option**: D. "The mean footwell intrusions for small and midsize cars are equal."- **Null Hypothesis (H₀)**: The mean footwell intrusions for small and midsize cars are equal.- **Alternative Hypothesis (H₁)**: The mean footwell intrusions for small and midsize cars are not equal.**Choice for Null Hypothesis (H₀)**: Option *D: "The mean footwell intrusions for small and midsize cars are equal."*#### Task 2: Determine Which Hypothesis is the Claim- **Which Hypothesis is the Claim?**: The null hypothesis, H₀, is the claim.#### Task 3: Decision Making- **Action**: Decide whether to reject or fail to reject the null hypothesis.- **Decision Outcome**: This will be based on calculated statistical evidence.#### Task 4: Interpretation in Context- **Interpretation**: Use statistical results to affirm if there's enough evidence to reject the actuary's claim.- **Significance Level (α)**: At 0.05, determine if there is sufficient evidence against the null hypothesis.### ConclusionBy following these steps, you'll conclude whether there is enough evidence to reject the insurance actuary's claim concerning footwell intrusions between small and midsize cars.

Name: ### Understanding Hypothesis Testing in Automotive SafetyAn insurance
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: ### Understanding Hypothesis Testing in Automotive SafetyAn insurance actuary claims that the mean footwell intrusions for small and midsize cars are equal. Crash tests at 35 mph were conducted on 9 small cars and 6 midsize cars. The footwell intrus

Here, the claim that the mean footwell instructions for small and midsize cars are equal. This is representing in null hypothesis. Hence, the correct claim is that the mean footwell instructions for small and midsize cars are equal. The hypotheses are given below: Null hypothesis: H0:µ1= µ2 Alternative hypothesis: H1:µ1≠ µ2 Here, the null hypothesis H0 is the claim.Step by step procedure to obtain test statistic and p-value using the MINITAB software: Choose Stat > Basic Statistics > 2-Sample t. Choose Summarized data. In first, enter Sample size as 9, Mean as 7, Standard deviation as 3.97. In second, enter Sample size as 6, Mean as 9, Standard deviation as 4.02. Choose Options. In Confidence level, enter 95. In Alternative, select not equal. Click OK in all the dialogue boxes. Output using the MINITAB software is given below: From the MINITAB output, the test statistic is –1.52 and the p-value is 0.160. Decision rule: If the P-value of the test is less than the level of significance, reject H0. Otherwise, fail to reject the null hypothesis H0. Conclusion: The level of significance is 0.05 and the P-value is 0.160. Here, P-value is greater than the level of significance. Thus, the decision is “ fail to reject the null hypothesis”. Therefore, there is evidence to conclude that the mean footwell instructions for small and midsize cars are equal. At the 50% significance level. there is no enough evidence to reject the insurance actuary’s claim.