Question

Twins In 2001, one county reported that, among 3132 white women who had babies, 94 were multiple births. There were also 20 multiple births to 606 black women. Does this indicate any racial difference in the likelihood of multiple births? a) Test an appropriate hypothesis and state your conclu- sion in context. b) If your conclusion is incorrect, which type of error did you commit?

Answer 1

(a)Yes, there is racial difference in the likelihood of multiple births.

nhere we want to test then

ull hypothesis H0:P1=P2 ( there is no racial difference) and

alternate hypothesis Ha:P1P2 ( there is racial difference)

we use z test and statistic z=|(p1-p2)|/SE(p1-p2)=0.0030/0.000062=48.71 is more than typical critical z(0.05/2)=1.96, so we reject the null hypothesis and conclude that there is racial difference in the likelihood of multiple births.

(b) since here we reject the null hypothesis so there is type I error commited

Type I error: Reject H0 when H0 is true

Type II error: Accept H0 when H0 is false

here following information has been generated for answering above question

difference of proportion
	sample	n	x	p=x/n	var(p)=p(1-p)/n
	white	3132	94	0.0300	0.000009
	black	606	20	0.0330	0.000053
	p1-p2=	-0.0030
	var(p1-p2)=	var(p1)+var(p2)=	0.000062
	SE(p1-p2)=	sqrt(var(p1-p2))=	0.0079
	z-value	margin of error	lower limit	upper limit
95% confidence interval	1.960	0.0154	-0.0184	0.0124