At a sobriety checkpoint the sheriff's department screened 676 drivers and 6 were arrested for DWI.Find the 92% confidence interval for the true proportion of drivers who were DWI that evening.
A)[0.000 0.027]
B)[0.003 0.015]
C)[0.902 0.938]
D)[0.000 0.076]
E)[0.006 0.030]

Question

Quizplus · Accepted Answer

We can use the formula for calculating the confidence interval for proportion:

p̂ ± z*√(p̂(1-p̂)/n)

where 
p̂ = 6/676 = 0.0089 (proportion of drivers arrested for DWI)
z = 1.75 (from the standard normal table for a 92% confidence interval)
n = 676

Substituting the values, we get:

0.0089 ± 1.75*√(0.0089*(1-0.0089)/676)

Simplifying, we get:

[0.0027, 0.0151]

Therefore, the 92% confidence interval for the true proportion of drivers who were DWI that evening is [0.003, 0.015]. The best choice is B.

At a Sobriety Checkpoint the Sheriff's Department Screened 676 Drivers