A simple random sample of front-seat occupants involved in car crashes is obtained. Among 3000 occupants not wearing seat belts, 36 were killed. Among 7697 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. 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? O A. Ho: P₁ ZP₂ H₁: Pg #P₂ OD. Ho: P₁ = P₂ H₁: P₁ #P₂ Identify the test statistic. z= (Round to two decimal places as needed.) Identify the P-value. P-value= (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? The appropriate confidence interval is (Round to three decimal places as needed.) What is the conclusion based on the confidence interval? The P-value is (1)- the significance level of a=0.05, so (2). the fatality rate is higher for those not wearing seat belts. b. Test the claim by constructing an appropriate confidence interval. |< (P₁-P₂) < Because the confidence interval limits (4) - OB. Ho: P₁ = P₂ H₁: P₁
A simple random sample of front-seat occupants involved in car crashes is obtained. Among 3000 occupants not wearing seat belts, 36 were killed. Among 7697 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. 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? O A. Ho: P₁ ZP₂ H₁: Pg #P₂ OD. Ho: P₁ = P₂ H₁: P₁ #P₂ Identify the test statistic. z= (Round to two decimal places as needed.) Identify the P-value. P-value= (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? The appropriate confidence interval is (Round to three decimal places as needed.) What is the conclusion based on the confidence interval? The P-value is (1)- the significance level of a=0.05, so (2). the fatality rate is higher for those not wearing seat belts. b. Test the claim by constructing an appropriate confidence interval. |< (P₁-P₂) < Because the confidence interval limits (4) - OB. Ho: P₁ = P₂ H₁: P₁
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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A simple random sample of front-seat occupants involved in car crashes is obtained. Among3000occupants not wearing seat belts,36were killed. Among 7697occupants wearing seat belts,18were killed. Use a0.05significance level to test the claim that seat belts are effective in reducing fatalities. Complete parts (a) through (c) below.
![### Educational Text on Hypothesis Testing and Confidence Intervals for Seat Belt Effectiveness
A simple random sample of front-seat occupants involved in car crashes is analyzed. The study includes data on 3000 occupants not wearing seat belts, where 36 were killed, and 7697 occupants wearing seat belts, where 18 were killed. A significance level of 0.05 is used to test the hypothesis that seat belts are effective in reducing fatalities.
#### a. Hypothesis Test
**Null and Alternative Hypotheses:**
- **H0 (Null Hypothesis):** \( p_1 = p_2 \)
- **H1 (Alternative Hypothesis):** \( p_1 \neq p_2 \)
Where \( p_1 \) represents the fatality rate of occupants not wearing seat belts, and \( p_2 \) represents the fatality rate of occupants wearing seat belts.
**Steps:**
1. **Identify the Test Statistic (z-value):**
Enter the calculated z-value: [_____].
*(Round to two decimal places as needed.)*
2. **Identify the P-value:**
Enter the calculated P-value: [_____].
*(Round to three decimal places as needed.)*
3. **Conclusion Based on Hypothesis Test:**
Evaluate the P-value with respect to the significance level, \(\alpha = 0.05\).
- If the P-value is (1) [less than/greater than] the significance level, (2) [fail to reject/reject] the null hypothesis.
- Based on this, determine if there is (3) [sufficient/insufficient] evidence to support the claim that the fatality rate is higher for those not wearing seat belts.
#### b. Constructing a Confidence Interval
**The Appropriate Confidence Interval:**
- Calculate and provide the interval for \( p_1 - p_2 \): [_____], [_____].
*(Round to three decimal places as needed.)*
**Conclusion Based on Confidence Interval:**
- Analyze if the confidence interval limits (4) [include/do not include] 0.
- If values are both (6) [positive and negative/only positive/only negative], evaluate if the fatality rate is (7) [higher/lower/the same] for those not wearing seat belts as compared to those wearing them.
#### c. Effectiveness of Seat Belts](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F717e652d-d2e5-48fc-b5bd-80fe3da265db%2Feb25251d-9795-45f8-9827-de775c4a4bae%2F60obkw_processed.png&w=3840&q=75)
Transcribed Image Text:### Educational Text on Hypothesis Testing and Confidence Intervals for Seat Belt Effectiveness
A simple random sample of front-seat occupants involved in car crashes is analyzed. The study includes data on 3000 occupants not wearing seat belts, where 36 were killed, and 7697 occupants wearing seat belts, where 18 were killed. A significance level of 0.05 is used to test the hypothesis that seat belts are effective in reducing fatalities.
#### a. Hypothesis Test
**Null and Alternative Hypotheses:**
- **H0 (Null Hypothesis):** \( p_1 = p_2 \)
- **H1 (Alternative Hypothesis):** \( p_1 \neq p_2 \)
Where \( p_1 \) represents the fatality rate of occupants not wearing seat belts, and \( p_2 \) represents the fatality rate of occupants wearing seat belts.
**Steps:**
1. **Identify the Test Statistic (z-value):**
Enter the calculated z-value: [_____].
*(Round to two decimal places as needed.)*
2. **Identify the P-value:**
Enter the calculated P-value: [_____].
*(Round to three decimal places as needed.)*
3. **Conclusion Based on Hypothesis Test:**
Evaluate the P-value with respect to the significance level, \(\alpha = 0.05\).
- If the P-value is (1) [less than/greater than] the significance level, (2) [fail to reject/reject] the null hypothesis.
- Based on this, determine if there is (3) [sufficient/insufficient] evidence to support the claim that the fatality rate is higher for those not wearing seat belts.
#### b. Constructing a Confidence Interval
**The Appropriate Confidence Interval:**
- Calculate and provide the interval for \( p_1 - p_2 \): [_____], [_____].
*(Round to three decimal places as needed.)*
**Conclusion Based on Confidence Interval:**
- Analyze if the confidence interval limits (4) [include/do not include] 0.
- If values are both (6) [positive and negative/only positive/only negative], evaluate if the fatality rate is (7) [higher/lower/the same] for those not wearing seat belts as compared to those wearing them.
#### c. Effectiveness of Seat Belts
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