Math Problem Statement
A simple random sample of front-seat occupants involved in car crashes is obtained. Among 2976 occupants not wearing seat belts, 34 were killed. Among 7639 occupants wearing seat belts, 18 were killed. Use a 0.05 significance level to test the claim that seat belts are effective in reducing fatalities. Complete parts (a) through (c) below. Question content area bottom Part 1 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? A. Upper H 0: p 1less than or equalsp 2 Upper H 1: p 1not equalsp 2 B. Upper H 0: p 1equalsp 2 Upper H 1: p 1not equalsp 2 C. Upper H 0: p 1equalsp 2 Upper H 1: p 1greater thanp 2 Your answer is correct.D. Upper H 0: p 1equalsp 2 Upper H 1: p 1less thanp 2 E. Upper H 0: p 1not equalsp 2 Upper H 1: p 1equalsp 2 F. Upper H 0: p 1greater than or equalsp 2 Upper H 1: p 1not equalsp 2 Part 2 Identify the test statistic. zequals 6.01 (Round to two decimal places as needed.) Part 3 Identify the P-value. P-valueequals 0.000 (Round to three decimal places as needed.) Part 4 What is the conclusion based on the hypothesis test? The P-value is less than the significance level of alphaequals0.05, 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 5 b. Test the claim by constructing an appropriate confidence interval. The appropriate confidence interval is enter your response hereless thanleft parenthesis p 1 minus p 2 right parenthesisless than enter your response here. (Round to three decimal places as needed.)
Solution
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Math Problem Analysis
Mathematical Concepts
Hypothesis Testing
Proportions
Statistical Significance
Confidence Intervals
Formulas
Z-test statistic formula for two proportions
Theorems
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Suitable Grade Level
Advanced Undergraduate
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