Question

11. Pet Ownership A recent random survey of households found that 14 out of 50 householders had a cat and 21 out of 60 householders had a dog. At a = 0.05, test the claim that fewer household owners have cats than household owners who have dogs as pets.

Answer 1

null Hypothesis:    Ho:    p1-p2		=	0.00
alternate Hypothesis: Ha:   p1-p2		<	0.00
for 0.05 level with left tailed test , critical value of z=			-1.645
Decision rule :                   reject Ho if test statistic z < -1.645
	Cat		Dogs
x1                =	14	x2                =	21
p̂1=x1/n1 =	14/50=0.2800	p̂2=x2/n2 =	21/60=0.3500
n1                       =	50	n2                       =	60
estimated prop. diff =p̂1-p̂2    =0.28-0.35 =		-0.0700
pooled prop p̂ =(x1+x2)/(n1+n2)=(14+21)/(50+60)=		0.3182
std error Se=√(p̂1*(1-p̂1)*(1/n1+1/n2) =		0.0892
test stat z=(p̂1-p̂2)/Se =(-0.07/0.0892)=		-0.78

since test statistic does not falls in rejection region we fail to reject null hypothesis

we do not have have sufficient evidence to conclude that proportion of cat owner are less than proportion of dog owners