Question

In: Statistics and Probability

An insurance company checks police records on 557 accidents selected at random and notes that teenagers...

An insurance company checks police records on 557 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 true percentage of accidents involving teenagers falls inside the confidence interval limits. B. We are 95% confident that the percent of accidents involving teenagers is 15.8%. C. 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) Explain what "95% confidence" means. About 95% of random samples of size will produce (1) that contain(s) the (2) of accidents involving teenagers.

Solutions

Expert Solution

(a) Here sample proportion = p^ = 88/557 = 0.1580

To construct 95% confidence interval, we need to calculate margin of error first

Margin of error = critical test statistic * standard error of sample proportion

critical test statistic for 95% confidence interval = NORMSDIST(0.975) = 1.96

Standard error of sample proportion = sqrt [0.1580 * (1 -0.1580)/557] = 0.03

95% confidence interval = 0.158 +- 0.03 = (0.128, 0.188)

(b) The interval means that We are 95% confident that the true percentage of accidents involving teenagers falls inside the confidence interval limits. Option A is correct .

(c) "95% confidence" means About 95% of random samples of size will produce that contain(s) the true mean proportion of accidents involving teenagers.


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