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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

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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).

Tasks:-
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.

Additional Questions.

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?

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tutor

tutor Added an answer on Jul 20,2019

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.

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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

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