# An insurance company checks police records on 560 accidents selected at random and notes that teenagers were at the wheel in 99 of them

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An insurance company checks police records on 560 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 the interpretation of the interval calculated above.

c. What does "95% confidence" means.

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?

The 95% confidence interval calculation, find the z score and apply the confidence interval formula.

p_hat +/-Z_score * sqrt(99/560 * (1 - 99/560)/560),

Obtain z score for 95 percent confidence interval using Excel, =NORM.S.INV(1-0.05/2)  = 1.96

0.177 +/- 1.96*sqrt(99/560 * (1 - 99/560)/560),

0.177 +/- 0.0316,  95% confidence interval (14.54 percent, 20.8 percent).

Explanation of the confidence interval.

We are​ 95% confident that the true percentage of accidents involving teenagers falls inside the confidence interval limits.

c.

About​ 95% of random samples of size

560

will produce

confidence intervals

that​ contain(s) the

true proportion

of accidents involving teenagers.

d.

The confidence interval  supports  the assertion of the politician. The figure quoted by the politician is  inside the interval.