Question

An insurance company checks police records on 591 accidents selected at random and notes that teenagers were at the wheel in 85 of them. Complete parts ​a) through d).

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

B) explain what your intervals mean

C) explain what 95% condifence means.

D) a politican urging tighter restrictions on drivers licenses issued to teens says, "In one of every five auto accidents, a teenager is being the wheel" Does your confidence interval supprt or contradict this statement? explain.

Answer 1

Proportion = 85 / 591 = 0.144

a)

95% confidence interval for p is

- Z/2 * Sqrt( p (1 - p) / n) < p < + Z/2 * Sqrt( p (1 - p) / n)

0.144 - 1.96 * sqrt( 0.144 * 0.856 / 591) < p < 0.144 + 1.96 * sqrt( 0.144 * 0.856 / 591)

0.116 < p < 0.172

95% confidence interval for p is ( 0.116 , 0.172) (11.6% , 17.2% )

b)

The given interval means that the bounds of confidence interval contains true proportion p.

c)

We are 95% confident that the true proportion p is between 0.116 and 0.172.

d)

Claimed proportion p = 1/5 = 0.2

Since 0.2 does not contain in confidence interval, the confidence interval contradicts this statement.