Question

In: Statistics and Probability

An insurance company checks police records on 556 accidents selected at random and notes that teenagers...

An insurance company checks police records on 556 accidents selected at random and notes that teenagers were at the wheel in 82 of them. Complete parts ​a) through ​d)

a) Construct the​ 95% confidence interval for the percentage of all auto accidents that involve teenage drivers. (Round to one decimal place as​ needed.)

b) Explain what your interval means.

c) Explain what​ "95% confidence" means.

d) 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?

Solutions

Expert Solution

a)

Standard error of the mean = SEM = √x(N-x)/N3 = 0.015

α = (1-CL)/2 = 0.025

Standard normal deviate for α = Zα = 1.960

Proportion of positive results = P = x/N = 0.147

Lower bound = P - (Zα*SEM) = 0.1

Upper bound = P + (Zα*SEM) = 0.2

b) Teenage proportion of accidents lie between 0.1 and 0.2

c) If we repeat the experiment, 95% times we will find that Teenage proportion of accidents lie between 0.1 and 0.2

d) Contradict as 20% is outside our interval


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