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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 α=0.1

The z-value is given by

zα2=z0.05=1.645

03

Compute the sample

For, z=1.645,p1=p2=0.5 andSE=.03

The sample is calculated as

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

Therefore, the required sample size is 1504.

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Most popular questions from this chapter

Assume that x is a binomial random variable with n = 1000 andp = 0.50. Use a normal approximation to find each of the following probabilities:

a. P(x>500)

b.P(490≤x<500)

c.P(x>550)

History of corporate acquisitions. Refer to the Academy of Management Journal (August 2008) investigation of the performance and timing of corporate acquisitions, Exercise 2.12 (p. 74). Recall that the investigation discovered that in a random sample of 2,778 firms, 748 announced one or more acquisitions during the year 2000. Does the sample provide sufficient evidence to indicate that the true percentage of all firms that announced one or more acquisitions during the year 2000 is less than 30%? Use a=0.05to make your decision.

Given that xis a hypergeometric random variable, computep(x)for each of the following cases:

a. N= 8, n= 5, r= 3, x= 2

b. N= 6, n= 2, r= 2, x= 2

c. N= 5, n= 4, r= 4, x= 3

Gouges on a spindle. A tool-and-die machine shop produces extremely high-tolerance spindles. The spindles are 18-inch slender rods used in a variety of military equipment. A piece of equipment used in the manufacture of the spindles malfunctions on occasion and places a single gouge somewhere on the spindle. However, if the spindle can be cut so that it has 14 consecutive inches without a gouge, then the spindle can be salvaged for other purposes. Assuming that the location of the gouge along the spindle is random, what is the probability that a defective spindle can be salvaged?

The “winner’s curse” in transaction bidding. In transaction bidding, the “winner’s curse” is the miracle of the winning (or loftiest) shot price being above the anticipated value of the item being auctioned. The Review of Economics and Statistics (Aug. 2001) published a study on whether shot experience impacts the liability of the winner’s curse being. Two groups of a stab in a sealed-shot transaction were compared (1)super-experienced stab and (2) less educated stab. In the super-experienced group, 29 of 189 winning flings were above the item’s anticipated value; 32 of 149 winning flings were above the item’s anticipated value in the less-educated group.

  1. Find an estimate of p1, the true proportion of super educated stab who fell prey to the winner’s curse
  2. Find an estimate of p2, the true proportion of less-educated stab who fell prey to the winner’s curse.
  3. Construct a 90 confidence interval for p1-p2.
  4. d. Give a practical interpretation of the confidence interval, part c. Make a statement about whether shot experience impacts the liability of the winner’s curse being.
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