Question

In a survey of 1000 drivers from Region A, 849 wear a seat belt. In a survey of 1000 drivers from Region B, 906 wear a seat belt. At a = 0.01, is there evidence to support the claim that the proportion of drivers who wear seat belts in Region A is less than the proportion of drivers who wear seat belts in Region B? Assume that the samples are random and independent. Complete parts (a) through (e) below. (a) Identify the claim and state Ho and H. Identify the claim. Let population 1 be drivers from Region A and let population 2 be drivers from Region B. Choose the correct answer below. O A. The claim is that the proportions of drivers who wear seat belts in both regions add up to 1. B. The claim is that the proportion of drivers who wear seat belts in Region A is greater than the proportion of drivers who wear seat belts in Region B. C. The claim is that the proportions of drivers who wear seat belts in both regions are equal. D. The claim is that the proportion of drivers who wear seat belts in Region A is less than the proportion of drivers who wear seat belts in Region B. State Ho and Hg. Choose the correct answer below. Click to select your answer(s).

Answer 1

Solution Given data Region A Region-B X = 849 906 he Tooo h = 1000 X2 P2 = ng 949 P2 = 906 P. 1ooo 1ooo Pi = 0.849 = 0.906 Pooled proportion Xitxa p= nithe 849+906 Pa 10ootlooo 1755 2000 p=0.8775 L = 0.01 (a) Toidentify the claim and state Ho and Ha Answer The claim is that the proportion of drivers who wear Seat belts in Region À is less than the propotion of drivers who Wear Seat belts in Region B. Therefore the l'option-D" is the correct answer

Now to state Ho and Ha: Nure hypothes is Ho: P, ZP2 Alternative hypothesis Ha: Pi<Pz This is "left-tailed" test Therefore the cloption- 'c" is the correct answer (b) To find the critical value and identify the rejection region: z critical Value = 2.33 There is one critical value Zo=(2.33) and one rejection region, 2 22.33 (c) Now to find the standardized test statistic We know that The formula of test Statistic , zis given by z = -P) 0.849 - 0.906 z = 0.8775 + 1ooo 1ooo) -0.057 z = 0.8775 (0.001+0.001)

-0.057 Z- 0.8775(1-0,8175) + food rooo -0.057 0.8775 X0.1285 (0.001+ 0.001) -0.057 Z 0.8775 X 0.1225 X 0.002 -0.057 0.000215 -0.057 0.0147 z = - 3.88 Test statistic Z -3.88 (d) since z is less than interejection eregion , fail to reject Ho (e) There is not enough evidence at the d = o.o level of significance claim that the proportion of drivers who Wear Seat belts in rejection A is less than the rejection B. to support the