Question

In: Statistics and Probability

An insurance company checks police records on 591 accidents selected at random and notes that teenagers...

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.

Solutions

Expert Solution

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.


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