Question

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.

Answer 1

(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.