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