Question

An insurance company checks police records on 594 accidents selected at random and notes that teenagers were at the wheel in 85 of them. Complete parts a) through

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.)

Answer 1

To construct the 95% confidence interval for the percentage of all auto accidents that involve teenage drivers, use the formula CI = p-hat ± Z * sqrt((p-hat * q-hat) / n) is (0.1126, 0.1734)

Step-by-step explanation:

To construct the 95% confidence interval for the percentage of all auto accidents that involve teenage drivers, we can use the formula:

CI = p-hat ± Z * sqrt((p-hat * q-hat) / n)

where:

p-hat = proportion of accidents involving teenage drivers = 85 / 594 = 0.1430

q-hat = 1 - p-hat = 1 - 0.1430 = 0.8570

n = sample size = 594

Z = Z-score corresponding to the desired confidence level (95%) = 1.96

Plugging in the values, we can calculate the confidence interval:

CI = 0.1430 ± 1.96 * sqrt((0.1430 * 0.8570) / 594)

= (0.1126, 0.1734)