Question

3. Are younger drivers more likely to have accidents in their driveways? Traffic engineers tabulated types of car accidents by drivers of various ages. Out of a total of 82,486 accidents involving drivers aged 15-24 years, 4243 of them occurred in a driveway. Out of a total of 219,170 accidents involving drivers aged 25-64 years, 10,701 of them occurred in a driveway. Use the 0.05 level of significance.

Answer 1

null Hypothesis:    Ho:    p1-p2		=	0.00
alternate Hypothesis: Ha:   p1-p2		>	0.00
for 0.05 level with right tailed test , critical value of z=			1.645
Decision rule :                   reject Ho if test statistic z > 1.645
	Younger		Older
x1                =	4243	x2                =	10701
p̂1=x1/n1 =	4243/82486 =0.0514	p̂2=x2/n2 =	10701/219170 =0.0488
n1                       =	82486	n2                       =	219170
estimated prop. diff =p̂1-p̂2    =		0.0026
pooled prop p̂ =(x1+x2)/(n1+n2)=(4243+10701)/(82486+219170) =		0.0495
std error Se=√(p̂1*(1-p̂1)*(1/n1+1/n2) =		0.0009
test stat z=(p̂1-p̂2)/Se =0.0026/0.0009 =		2.95

since test statistic falls in rejection region we reject null hypothesis
we have sufficient evidence to conclude that younger drivers are more likely to have accidents in their driveways