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 3,477 vehicles counted, 877 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.

Appendix A Statistical Tables

(Round your answers to 3 decimal places.)

a. The point estimate is   .
b.   ≤ p ≤  

Answer 1

A)

Point estimate = 877/3477 = 0.252

B)

N = 3477

P = 0.252

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 877

N*(1-p) = 2600

Both the conditions are met so we can use standard normal z table to estimate the interval

Critical value z from z table.for 99% confidence level is 2.58

Margin of error (MOE) = Z*√{P*(1-P)}/√N

After substitution

MOE = 0.01899627420

Interval is given by

P-MOE < P < P+MOE

0.233 < P < 0.271