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Chapter 6: Q72E (page 364)

Study of aircraft bird strikes. Refer to the InternationalJournal for Traffic and Transport Engineering(Vol. 3,2013) study of aircraft bird strikes at a Nigerian airport,Exercise 6.54 (p. 357). Recall that an air traffic controller

wants to estimate the true proportion of aircraft bird strikesthat occur above 100 feet. Determine how many aircraftbird strikes need to be analyzed to estimate the true proportionto within .05 if you use a 95% confidence interval.

Short Answer

Expert verified

227 aircraft bird strikes need to be analyzed to estimate the true proportion to within .05

Step by step solution

01

Given information

Referring to ,Exercise 6.54 (p. 357)

02

Finding the sample size

Here the sample proportion isp^=3644=0.82

q^=1−p^=1−0.82=0.18

Here the standard error is 0.05

The critical value for a 95% confidence interval iszα/2=z0.05/2=z0.025=1.96

SE=zα/2p^q^nn=z2α/2p^q^SE2n=1.962×0.82×0.180.052n=226.81n≈227

The required sample size is 227.

227 aircraft bird strikes need to be analyzed to estimate the true proportion to within .05

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Most popular questions from this chapter

Evaporation from swimming pools. A new formula for estimating the water evaporation from occupied swimming pools was proposed and analyzed in the journal Heating Piping/Air Conditioning Engineering (April 2013). The key components of the new formula are number of pool occupants, area of pool’s water surface, and the density difference between room air temperature and the air at the pool’s surface. Data were collected from a wide range of pools for which the evaporation level was known. The new formula was applied to each pool in the sample, yielding an estimated evaporation level. The absolute value of the deviation between the actual and estimated evaporation level was then recorded as a percentage. The researchers reported the following summary statistics for absolute deviation percentage: x¯=18, s=20. Assume that the sample containedn=15 swimming pools

a. Estimate the true mean absolute deviation percentage for the new formula with a 90% confidence interval.

b. The American Society of Heating, Refrigerating, and Air-Conditioning Engineers (ASHRAE) handbook also provides a formula for estimating pool evaporation. Suppose the ASHRAE mean absolute deviation percentage is μ=40%. (This value was reported in the article.) On average, is the new formula “better” than the ASHRAE formula? Explain

Question: The mean and standard deviation of a random sample of n measurements are equal to 33.9 and 3.3, respectively.

a. Find a 95% confidence interval for μif n = 100.

b. Find a 95% confidence interval forμ if n = 400.

c. Find the widths of the confidence intervals found in parts a and b. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient fixed?

U.S. Postal Service’s performance. The U.S. Postal Service (USPS) reports that 95% of first-class mail within the same city is delivered on time (i.e., within 2 days of the time of mailing). To gauge the USPS performance, Price Waterhouse monitored the delivery of first-class mail items between Dec. 10 and Mar. 3—the most difficult delivery season due to bad weather conditions and holidays. In a sample of 332,000 items, Price Waterhouse determined that 282,200 were delivered on time. Comment on the performance of USPS first-class mail service over this time period.

Jitter in a water power system. Jitter is a term used to describe the variation in conduction time of a water power system. Low throughput jitter is critical to successful waterline technology. An investigation of throughput jitter in the opening switch of a prototype system (Journal of Applied Physics) yielded the following descriptive statistics on conduction time for n = 18 trials:x=334.8 nanoseconds, s = 6.3 nanoseconds. (Conduction time is defined as the length of time required for the downstream current to equal 10% of the upstream current.)

a. Construct a 95% confidence interval for the true standard deviation of conduction times of the prototype system.

b. Practically interpret the confidence interval, part a.

c. A system is considered to have low throughput jitter if the true conduction time standard deviation is less than 7 nanoseconds. Does the prototype system satisfy this requirement? Explain.

Explain what is meant by the statement, “We are 95% confident that an interval estimate contains μ.”
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