Question

The highway department wants to estimate the proportion of vehicles on Interstate 25 between the hours of midnight and 5:00 A.M. that are 18-wheel tractor trailers. The estimate will be used to determine highway repair and construction considerations and in highway patrol planning. Suppose researchers for the highway department counted vehicles at different locations on the interstate for several nights during this time period. Of the 3,367 vehicles counted, 971 were 18-wheelers.

a. Determine the point estimate for the proportion of vehicles traveling Interstate 25 during this time period that are 18-wheelers.
b. Construct a 99% confidence interval for the proportion of vehicles on Interstate 25 during this time period that are 18-wheelers.

(Round your answers to 3 decimal places.)

a. The point estimate is __________
b. _______ ≤ p ≤ ________

Answer 1

a)

The point estimate = 971/3367 = 0.2884

b)

sample size, n = 3367
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.2884 * (1 - 0.2884)/3367) = 0.008

Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, Zc = Z(α/2) = 2.58

Margin of Error, ME = zc * SE
ME = 2.58 * 0.008
ME = 0.0206

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.2884 - 2.58 * 0.008 , 0.2884 + 2.58 * 0.008)
CI = (0.268 , 0.309)

0.268 <= p < = 0.309