In a survey of 480 divers from the South, 407 wear a seat belt, in a survey of 3

Question

In a survey of 480 divers from the South, 407 wear a seat belt, in a survey of 370 drivers from the Northeast 282 wear a seat belt. At a = 0.05 can you support the claim that the proportion of drivers who wear seat belts is greater in the South than in the Northeast? Assume the random samples are independent. Complete parts (s) through (e). (a) identify the claim and state H_0 and H_a. The claim is "the proportion of drivers who wear seat belts in the South is (1) ___ in the Northeast." Let p_1 represent the population proportion for the South, and p_2 represent the population proportion for the Northeast State H_0 and H_a Choose the correct answer A. H_0: p_1 notequalto p_2 H_a: p_1 = p_2 B. H_0: p_1 > p_2 H_a: p_1 lessthanorequalto p_2 C. H_0: p_1 = p_2 H_a: p_1 notequalto p_2 D. H_0: p_1 greaterthanorequalto p_2 H_a: p_1

Explanation / Answer

(a) H0 : The proportion of drivers who wear seat belts in the south is equal in the northeast. p1 <= p2

Ha : The proportion of drivers who wear seat belts in the south is more in the northeast. p1 > p2

so answer is option F.

(b) critical value for alpha = 0.05 is Zcritical = 1.96

(c) Rejection region

z > 1.645 for one tailed Z - test

(d) Standard Test Statistic

p1 = 407/480 = 0.848

n1 = 480

p2 = 282/ 370 = 0.7622

n2 = 370

pooled estimate p* = ( 407 + 282)/ ( 480 + 370) = 0.8106

Standard Error SE0 = sqrt [ p* (1-p*) (1/n1 +1/n2 )] = sqrt [ 0.8106 * 0.1894 * (1/480 + 1/370) ] = 0.0271

Z = (p1 -p2 )/ SE0 = (0.848-0.7622)/0.0271 = 3.166

(d) Reject Null Hypothesis because the test statistic in the rejection region.because Z > Zcritical

(e) At the 5% significance level, there is sufficient evidence to support the claim.

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