An insurance company checks police records on 593 accidents selected at random a

Question

An insurance company checks police records on 593 accidents selected at random and notes that teenagers were at the wheel in 82 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 a randomly sampled accident would involve a teenager a percent of the time that falls inside the confidence interval limits. B. We are 95% confident that the percent of accidents involving teenagers is 13.8%. 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 593 will produce (1) ____ that contain(s) the (2) ___ of accident 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? A. The confidence interval supports the assertion of the politician. The figure quoted by the politician is outside the interval. B. The confidence interval contradicts the assertion of the politician. The figure quoted by the politician is inside the interval. C. The confidence interval contradicts the assertion of the politician. The figure quoted by the politician is outside the interval. D. The confidence interval supports the assertion of the politician. The figure quoted by the politician is inside the interval. (1) a true proportion confidence intervals a sample proportion (2) sample proportion confidence interval true proportion

Explanation / Answer

The statistical software output for this problem is:

One sample proportion summary confidence interval:
p : Proportion of successes
Method: Standard-Wald

95% confidence interval results:

Hence,

95% confidence interval will be:

(11.0%, 16.6%)

b) Option C

c) confidence intervals; true proportions

d) Option C

Proportion Count Total Sample Prop. Std. Err. L. Limit U. Limit p 82 593 0.13827993 0.0141754 0.11049666 0.16606321

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