Question

An insurance company checks police records on 559 accidents selected at random and notes that teenagers were at the wheel in 92 of them. Construct the​ 95% confidence interval for the percentage of all auto accidents that involve teenage drivers.

Question: 95% CI= (___%,___%) (round to one decimal place as needed.)

Answer 1

Sample proportion = 92 / 559 = 0.165

95% confidence interval for p is

- Z/2 * sqrt [ (1 - ) / n ] < p < + Z/2 * sqrt [ (1 - ) / n ]

0.165 - 1.96 * sqrt [ 0.165 * ( 1 - 0.165 ) / 559] < p < 0.165 + 1.96 * sqrt [ 0.165 * ( 1 - 0.165 ) / 559]

0.134 < p < 0.196

95% CI is (13.4% , 19.6% )