An insurance company checks police records on 564 accidents selected at random a

Question

An insurance company checks police records on 564 accidents selected at random and notes that teenagers were at the wheel in 88 of them. 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. A. We are 95% confident that the percent accidents involving teenagers is 15.6%. B. 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 C. 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 564 will produce that contain(s) the of accidents involving d) A politician urging tighter restrictions on drivers licenses issued to says. 'In one of every five auto accidents, a teenager is behind the wheel' Does the statement? A. The confidence interval contradicts the assertion of the politician. The figure quoted by the politician is outside the interval. B. The interval supports the assertion of the politician. The figure quoted by the politician is inside the interval. C. The confidence interval supports the assertion of the politician. The figure quoted by the politician is outside the interval.

Explanation / Answer

P =88/564 =0.1560

Z value for 95% = 1.96

CI=P±sqrt(P*(1-P) /n)

CI =0.1560 ± sqrt(0.1560(1-0.1560) /564

            =0.1560 ±0.01528

            =(0.1407, 0.1713 )

0.1< P < 0.2

            =14.07% ,17.13%

b)

option C is correct

c)

confidence intervals

true proportion

d)

option A is correct

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