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3. Are younger drivers more likely to have accidents in their driveways? Traffic engineers tabulated types...

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3. Are younger drivers more likely to have accidents in theirdriveways? Traffic engineers tabulated types of car accidents bydrivers of various ages. Out of a total of 82,486 accidentsinvolving drivers aged 15-24 years, 4243 of them occurred in adriveway. Out of a total of 219,170 accidents involving driversaged 25-64 years, 10,701 of them occurred in a driveway. Use the0.05 level of significance.

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3.6 Ratings (667 Votes)

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
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