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Chapter 8: Q72E (page 452)

Traffic sign maintenance. Refer to the Journal of Transportation Engineering (June 2013) study of traffic sign maintenance in North Carolina, Exercise 8.54 (p. 489). Recall that the proportion of signs on NCDOT-maintained roads that fail minimum requirements was compared to the corresponding proportion for signs on county-owned roads. How many signs should be sampled from each maintainer to estimate the difference between the proportions to within .03 using a 90% confidence interval? Assume the same number of signs will be sampled from NCDOT-maintained roads and county-owned roads

Short Answer

Expert verified

The required sample size is 1504.

Step by step solution

01

Given Information

The confidence coefficient is 0.90

The sampling error is

SE=.03

02

Z-value

For 伪=0.1

The z-value is given by

z伪2=z0.05=1.645

03

Compute the sample

For, z=1.645,p1=p2=0.5鈥�andSE=.03

The sample is calculated as

n1=n2=z0.052脳p11-p1+p21-p2SE2=1.6452脳0.25+0.250.032=2.706025脳.50.0009=1.35300.0009=1503.33鈮�1504

Therefore, the required sample size is 1504.

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