### Hypothesis Testing and Confidence Intervals in Car Crash Fatality Rates#### Problem Statement:A simple random sample of front-seat occupants involved in car crashes is obtained. Among 2,732 occupants not wearing seat belts, 36 were killed. Among 7,859 occupants wearing seat belts, 17 were killed. Use a 0.01 significance level to test the claim that seat belts are effective in reducing fatalities. Complete parts (a) through (c) below.### Part (a): Test the claim using a hypothesis test.Consider the first sample to be the sample of occupants not wearing seat belts and the second sample to be the sample of occupants wearing seat belts. **Question:** What are the null and alternative hypotheses for the hypothesis test?**Options for Hypotheses:**- A. \( H_0: p_1 = p_2 \) \( H_1: p_1 < p_2 \)- B. \( H_0: p_1 \neq p_2 \) \( H_1: p_1 = p_2 \)- C. \( H_0: p_1 = p_2 \) \( H_1: p_1 \neq p_2 \)- D. \( H_0: p_1 \neq p_2 \) \( H_1: p_1 = p_2 \)- E. \( H_0: p_1 \neq p_2 \) \( H_1: p_1 > p_2 \)- F. \( H_0: p_1 = p_2 \) \( H_1: p_1 > p_2 \) *(Correct)*### Hypothesis Test Results:- **Identify the test statistic:** \( z = 7.02 \) *(Round to two decimal places as needed.)* - **Identify the P-value:** \( \text{P-value} = 0 \) *(Round to three decimal places as needed.)*- **Conclusion Based on Hypothesis Test:** The P-value is less than the significance level \( \alpha = 0.01 \), so reject the null hypothesis. There is sufficient evidence to support the claim that the fatality rate is higher for those not wearing seat belts.### Part (b): Test the claim by constructing an ### Hypothesis Testing and Confidence IntervalsIn this section, we will go over how to identify and evaluate statistical test results.#### Identify the Test StatisticThe value of the test statistic is given by:\[ z = 7.02 \](Round to two decimal places as needed.)#### Identify the P-valueThe P-value is calculated as follows:\[ P\text{-value} = 0 \](Round to three decimal places as needed.)#### Conclusion Based on the Hypothesis TestTo make a decision based on the hypothesis test, we compare the P-value to the significance level (α):The P-value is **less than** the significance level of \( \alpha = 0.01 \), so we:**reject** the null hypothesis. There **is** sufficient evidence to support the claim.#### Construct an Appropriate Confidence IntervalNext, we will test the claim by constructing an appropriate confidence interval for the difference between two population proportions (\(p_1 - p_2\)):The appropriate confidence interval is:\[ \Box < (p_1 - p_2) < \Box \](Round to three decimal places as needed.)This process ensures that we have a clear understanding of how to interpret statistical results and apply them to hypotheses testing. Use the tools provided in this module to help solve similar problems and view examples for further understanding.**Interactive Options:**- [Help me solve this](#)- [View an example](#)- [Get more help](#)- [Media](#)

Given Information: Sample 1: n1=2732 x1=36 Sample 2: n2=7859 x2=17 Significance level α=0.01

A simple random sample of front-seat occupants involved in car crashes is obtained. Among 2732 occupants not wearing seat belts, 36 were killed. Among 7859 occupants wearing seat belts, 17 were killed. Use a 0.01 significance le the claim that seat belts are effective in reducing fatalities. Complete parts (a) through (c) below. CI a. Test the claim using a hypothesis test. Consider the first sample to be the sample of occupants not wearing seat belts and the second sample to be the sample of occupants wearing seat belts. What are the null and alternative hypotheses for the hypothesis test? OA Ho: P₁ P2 OB. Ho: P₁ P2 OC. Ho: P₁ P₂ H₁: P₁ P₂ H₁: P₁ P₂ H₁: P₁ P₂ F. Ho: P1 P2 OE Ho: P₁ OD. Ho: P₁ SP₂ P₂ H₁: P₁ P2 H₁: P₁ P₂ H₁: P₁ P₂2 Identify the test statistic. z = 7.02 (Round to two decimal places as needed.) Identify the P-value. P-value = 0 (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? is sufficient evidence support the claim that the fatality rate is higher for those not wearing seat belts. the null hypothesis. There less than the significance level of a = 0.01, so The P-value is reject b. Test the claim by constructing an appropriate confidence interval. The appropriate confidence interval is < (P₁-P₂) <-

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 1GP