Question

1. A study compared patients who suffered a heart attack in the daytime with patients who suffered a heart attack in the night.  Of 58,593 had a heart attack in the daytime 11,604 survived.  Of 28,155 who had a heart attack at night 4139 survived.  Use α = .01 and test the claim that the survival rates are the same.

Answer 1

null Hypothesis:    Ho:    p1-p2		=	0.00
alternate Hypothesis: Ha:   p1-p2		≠	0.00
for 0.01 level with two tailed test , critical value of z=			2.576
Decision rule :                   reject Ho if absolute value of test statistic |z|>2.576
	daytime		night time
x1                =	11604	x2                =	4139
p̂1=x1/n1 =	0.1980	p̂2=x2/n2 =	0.1470
n1                       =	58593	n2                       =	28155
estimated prop. diff =p̂1-p̂2    =0.1980-0.1470 =		0.0510

pooled prop p̂ =(x1+x2)/(n1+n2)=(11604+4139)/(58593+28155)=		0.1815
std error Se=√(p̂1*(1-p̂1)*(1/n1+1/n2) =sqrt(0.1815*(1-0.1815)*(1/58593+1/28155)=		0.0028

test stat z=(p̂1-p̂2)/Se =0.0510/0.0028 =

18.26

since test statistic falls in rejection region we reject null hypothesis

we have sufficient evidence to conclude that t the survival rates are different