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Question Help A simple random sample of front seat occupants involved in car crashes is obtained. Among 2923 occupants not wearing seat belts. 32 were killed. Among 7872 occupants wearing seat belts, 11 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: Pusp2 Hy: P+P2 OD. Ho D-D2 Hi. Pi>P2 OB. HOP, #P2 HP P2 O E. Ho: P = P2 H₂: P1 P2 O C. Ho: P1 P2 HP*P2 OF. Ho: P1 P2 HP1P2 Identify the test statistic sufficient (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 P-value is the significance level of a = 0.05, 50 the null hypothesis. There evidence to support the claim that the fatality rate is higher for those not wearing seat belts. b. Test the claim by constructing an appropriate confidence interval The appropriate confidence interval is < (91-92) O (Round to three decimal places as needed) What is the conclusion based on the confidence interval? Because the confidence interval limits 0 it appears that the two fatality rates are confidence interval limits include values, it appears that the fatality rate is wearing seat belts c. What do the results suggest about the effectiveness of seat belts? Because the for those not A. The results suggest that the use of seat belts is associated with lower fatality rates than not using seat belts. B. The results suggest that the use of seat belts is associated with higher fatality rates than not using seat belts. OC. The results suggest that the use of seat belts is associated with the same fatality rales as not using seat belts. OD. The results are inconclusive

Answer 1

= For sample 1, we have that the sample size is Ni = 2923, the number of favorable cases is Xi 32, so then the sample proportion is p1 = * = 2323 = 0.0109 For sample 2, we have that the sample size is Ng = 7872, the number of favorable cases is X2 11, so then the sample proportion is p2 = x = 1872 = 0.0014 The value of the pooled proportion is computed as p = *. -X 2923+7872 0.004 Also, the given significance level is a = 0.05. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: 324-11 Ho: p1 = P2 Ha: Pi>p2 This corresponds to a right-tailed test, for which a z-test for two population proportions needs to be conducted. (2) Rejection Region Based on the information provided, the significance level is a = 0.05, and the critical value for a right-tailed test is ze = 1.64. The rejection region for this right-tailed test is R={z:x> 1.64} (3) Test Statistics The Z-statistic is computed as follows: P1 - 2 (1-)(1/nı +1/ne) 0.0109 - 0.0014 0.004- (1 -0.004)(1/2923 +1/7872) 7 (4) Decision about the null hypothesis Since it is observed that z = 7> ze = 1.64, it is then concluded that the null hypothesis is rejected Using the P-value approach: The p-value is p = 0, and since p = 0 <0.05, it is concluded that the null hypothesis is rejected. (5) Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population proportion p1 is greater than p2, at the 0.05 significance level.

1.96. The corresponding confidence interval is The critical value for a = 0.05 is me = %1-a/2 computed as shown below: CI 3 -P2 P1(1-P) N + P2(1 - 02) N. , 1 - 2 + 1 Pi(1 - Pi) P2(1 - P2) N NO + 0.001(1 - 0.001 0.011 0.011(1 0.011) 0.001 - 1.96 x V 2923 0.001(1 -0.001) ,0.011 -0.001 +1.96 x 7872 0.011(1 0.011 2923 7872 = 0.006 <P - P2 <0.013,

Question Help A simple random sample of front seat occupants involved in car crashes is obtained. Among 2923 occupants not wearing seat belts. 32 were killed. Among 7872 occupants wearing seat belts, 11 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 HOP SP2 Hy: P1 P2 OB. HOP, #P2 HP P2 O E. Ho: P = P2 H₂: P1 P2 O C. Ho: P1 P2 HP*P2 OF. Ho: P1 P2 HP1P2 ун, р, гр. Hi Pi>P2 Identify the test statistic 2- 7.00 (Round to two decimal places as needed.) Identify the P-value P-value=0.000 (Round to three decimal places as needed.) What is the conclusion based on the hypothesis test? less than reject is The P-value is the significance level of a = 0.05, 50 the null hypothesis. There sufficient evidence to support the claim that the fatality rate is higher for those not wearing seat belts. b. Test the claim by constructing an appropriate confidence interval 0.006 0.013 The appropriate confidence interval is (P1-P2) (Round to three decimal places as needed) What is the conclusion based on the confidence interyal? different are greater than Because the confidence interval limits 0, it appears that the two fatality rates are Because the confidence interval limits include positive values, it appears that the fatality rate is for those not wearing seat belts greater c. What do the results suggest about the effectiveness of seat belts? etésults suggest that the use of seat belts is associated with lower fatality rates than not using seat belts. B. The results suggest that the use of seat belts is associated with higher fatality rates than not using seat belts. OC. The results suggest that the use of seat belts is associated with the same fatality rales as not using seat belts. OD. The results are inconclusive