Asimple random sample of front-seat occupants involved car crashe is obtained Am

Question

Asimple random sample of front-seat occupants involved car crashe is obtained Among 2g220coupants not earing seatbelts, 28 were kaed. Among 7602 ocoupants wearing seat belts, 16 were killed use a 001 sianreanoelevelto tost the dam that seat belts are efective in reduong fataliter. Complete parts a)through (c)below. He pa ldently the best statistic. (Round to two decimal plaoes as needed (Round to three decimal places as needed) What is tha conclusion based on the hypothesis test? the nul hypothesis There suficienteidenoetosupportthro claim that the fatality rate is higher for those not wearing seat belts b. claim by an appropriate oonfidence inerval. The approprale cordente interval is Round deo needed

Explanation / Answer

1) option A) is correct

2) n1 = 2922 x1 = 28 n2 = 7602 x2 = 22

p =(16+22)/(2922+7602) = 38/10524

z = (28/2922 - 22/7602)/(sqrt(38/10524 *10486 /10524 *(1/2922 +1/7602))

=5.12302

3)p-value = P(z>5.123) =0

p-value is less than alpha, hence we reject the null , there is sufficient evidence

4) p1^ -p2^ = 28/2922 - 22/7602 =0.00668

sqrt(p1*q1/n1 + p2q2/n2) = sqrt(28/2922*2894/2922+22/7602*7580/7602) =0.111248

z0.005 = 2.575

hence required confidence interval is

(0.00668 - 2.575*0.111248,0.00668 + 2.575*0.111248)

(-0.279783, 0.293143)

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