Teens ages 1520 make up 10 of the driving population The ins

Teens, ages 15-20 make up 10% of the driving population. The institute found that 14% of accidents involve teenage drivers. Suppose that this percentage was based on examining records from 500 randomly selected accidents. Does the study provide convincing evidence that the proportion of accidents involving teenage drivers from .10, the proportion of teens in the driving population? Assume the necessary conditions hold.

Solution

Set Up Hypothesis
Null, H0:P=0.1
Alternate, H1: P!=0.1
Test Statistic
No. Of Success chances Observed (x)=70
Number of objects in a sample provided(n)=500
No. Of Success Rate ( P )= x/n = 0.14
Success Probability ( Po )=0.1
Failure Probability ( Qo) = 0.9
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.14-0.1/(Sqrt(0.09)/500)
Zo =2.9814
| Zo | =2.9814
Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo| =2.981 & | Z | =1.96
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != 2.98142 ) = 0.00287
Hence Value of P0.05 > 0.0029,Here we Reject Ho