Question

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?

Answer 1

a)

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

α = (1-CL)/2 = 0.025

Standard normal deviate for α = Z_α = 1.960

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

Lower bound = P - (Z_α*SEM) = 0.1

Upper bound = P + (Z_α*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