Question

An insurance company checks police records on 563 accidents selected at random and notes that teenagers were at the wheel in 99 of them. Complete parts a) through d).

a) Construct the 95% confidence interval for the percentage of all auto accidents that involve teenage drivers.

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.

confidence interval : [ p - z*(p*(1-p)/n)^0.5 , p + z*(p*(1-p)/n)^0.5 ]

for 95% confidence interval z=1.96

p = 99/563

95% confidence interval : [ 0.1758 - 1.96*( 0.1758*(1- 0.1758)/563)^0.5 , 0.1758 + 1.96*( 0.1758 *(1- 0.1758 )/563)^0.5 ]

= [ 0.1444 , 0.2072 ]

95% confidence interval for percentage = [14.44% , 20.72%]

b.

the interval mean that we are 95% sure that the percentage of all auto accidents that involve teenage drivers is between 14.44% and 20.72%

c.

95% confidence means that the probability that the percentage of all auto accidents that involve teenage drivers is between 14.44% and 20.72% is 95% or 0.95

P(percentage of all auto accidents that involve teenage drivers is between 14.44% and 20.72%) = 0.95

d.

1 out of 5 = 1/5 = 0.20 = 20%

percentage quouted by politician = 20%

the 95% confidence interval : [14.44% , 20.72%]

20% lies in the confidence interval so the confidence interval agrees with the politician