An insurance company checks police records on 595 accidents

An insurance company checks police records on 595 accidents selected at random and notes that teenagers were at the wheel in 97 of them. Construct the 95% confidence interval for the percentage of all auto accidents that involve teenage drivers. Explain what your interval means. We are 95% confident that the true percentage of accidents involving teenagers falls inside the confidence interval limits. We are 95% confident that a randomly sampled accident would involve a teenager a percent of the time that falls inside the confidence interval limits. C. We are 95% confident that the percent of accidents involving teenagers is 16.3%. Explain what \"95% confidence\" means. About 95% of random samples of size 595 will produce that contain(s)the of accidents involving teenagers. A politician urging tighter restrictions on drivers\' licenses issued to teens says, In one of every five auto accidents, a teenager is behind the wheel.\" Does the confidence interval support or contradict this statement? The confidence interval supports the assertion of the politician. The figure quoted by the politician is outside the interval. The confidence interval supports the assertion of the politician. The figure quoted by the politician is inside the interval. The confidence interval contradicts the assertion of the politician. The figure quoted by the politician is inside the interval. The confidence interval contradicts the assertion of the politician. The figure quoted by the politician is outside the interval

Solution

a)
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=97
Sample Size(n)=595
Sample proportion = x/n =0.163
Confidence Interval = [ 0.163 ±Z a/2 ( Sqrt ( 0.163*0.837) /595)]
= [ 0.163 - 1.96* Sqrt(0) , 0.163 + 1.96* Sqrt(0) ]
= [ 0.133,0.193]~ [ 0.2,0.2 ]

b)
Option A

d)
one of evry 5 accidents is behind the wheel = 1/ 5 = 0.20
0.20 is outside the interval commpute, [ 0.133,0.193]
Option d