Question

An insurance company checks police records on 562 accidents selected at random and notes that teenagers were at the wheel in 81 of them. Complete parts ​a) through ​d).

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

​95% CI = ( ___________ %, _________ % )

​(Round to one decimal place as​ needed.)

​b) Explain what your interval means.

1. We are​ 95% confident that a randomly sampled accident would involve a teenager a percent of the time that falls inside the confidence interval limits.
2. We are​ 95% confident that the percent of accidents involving teenagers is 14.4​%.
3. We are​ 95% confident that the true percentage of accidents involving teenagers falls inside the confidence interval limits.

​c) Explain what​ "95% confidence" means.

About​ 95% of random samples of size 562 will produce (1) __________ that​ contain(s) the

(2) _________   of accidents involving teenagers.

​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?

1. The confidence interval supports the assertion of the politician. The figure quoted by the politician is inside the interval.
2. The confidence interval contradicts the assertion of the politician. The figure quoted by the politician is outside the interval.
3. The confidence interval supports the assertion of the politician. The figure quoted by the politician is outside the interval.
4. The confidence interval contradicts the assertion of the politician. The figure quoted by the politician is inside the interval.

(1)

• confidence intervals
• a true proportion
• a sample proportion

(2)

• true proportion
• sample proportion
• confidence interval

Please show all of the math. Thank you!

Answer 1