Question

8.13 The following results show the relationship between smoking in mothers and the survival of newborns past their first year. Use the bino- mial test to determine if the proportion of newborns that died in the first year is lower in nonsmokers than smokers. Non-smoker Smoker Died in 1st year Alive at 1 year 28 5606 583

Answer 1

ho: there is no significant difference in the proportion of new born that died in the 1st year between non smoker and smoker. p1 = p2
h1: the proportion of new born that died in the 1st year for non smoker is less than smoker. p1 < p2

	non smoker	smoker
x	28	7
n	5614	590
p =x/n	0.0050	0.0119

p = (p1 * n1 + p2 * n2) / (n1 + n2)
p = (0.005*5614+0.0119*590)/(5614+590)
p = 0.00570

SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
SE = SQRT(0.0057*(1-0.0057)*(1/5614+1/590))
SE = 0.003

z = (p1 - p2) / SE
z = (0.005-0.0119)/0.003258
z = -2.118

p-value = P(Z<z)
p-value = P(z<-2.117864)
p-value = NORMSDIST(-2.117864)
p-value = 0.017093294

With (z=-2.118, p<5%), i reject Ho at 5% level of significance and conclude that the proportion of new born that died in the 1st year for non smoker is less than smoker. p1 < p2