a) An insurance company regularly reviews official police reports of traffic acc

Question

a) An insurance company regularly reviews official police reports of traffic accidents in a particular region of the country so that it can price its premiums in that region appropriately. A review of a random sample of 582 accident reports showed that in 91 accidents, a teenage driver was found to be at fault. Report the upper bound of a 90% confidence interval for the true proportion of accidents in the area that are caused by teenagers, to three decimal places. Take all calculations toward the answer to four (4) decimal places.

Explanation / Answer

The confidence interval of the proportion is given as

p +- Z* sqrt(pq/n) , where q = 1-p and

p = 1/91 = 0.01 , so q = 1- 0.01 = 0.99

also the z value for the 90% confidence interval is 1.645 , using the z tables

0.01 +- 1.645*sqrt(0.01*0.99/582)

solving this , the confidence interval is as follows

0.0167 , 0.0032

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