Question

The Idaho Department of Law Enforcement, in conjunction with the federal government, recently began a truck inspection program in Idaho. The current inspection effort is limited to an inspection of only those trucks that visually appear to have some defect when they stop at one of the weigh stations in the state. The proposed inspection program will not be limited to the trucks with visible defects, but will potentially subject all trucks to a comprehensive safety inspection.

Jane Lund of the Department of Law Enforcement is in charge of the new program. She has stated that the ultimate objective of the new truck inspection program is to reduce the number of trucks with safety defects operating in Idaho. Ideally, all trucks passing through, or operating within Idaho would be inspected once a month, and substantial penalties would be applied to operators if safety defects were discovered. Ms. Lund is confident that such an inspection program would, without fail, reduce the number of defective trucks operating on Idaho’s highways. However, each safety inspection takes about an hour, and because of limited money to hire inspectors, she realizes that all trucks cannot be inspected. She also knows it is unrealistic to have trucks wait to be inspected until trucks ahead of them have been checked. Such delays would cause problems with the drivers.

In meetings with her staff, Jane has suggested that before the inspection program begins, the number of defective trucks currently operating in Idaho should be estimated. This estimate can be compared with later estimates to see if the inspection program has been effective. To arrive at this initial estimate, Jane thinks that some sort of sampling plan to select representative trucks from the population for all trucks in the state must be developed. She has suggested that this sampling be done at the eight weigh stations near Idaho’s borders, but she is unsure how to establish a statistically sound sampling plan that is practical to implement.

Answer 1

Answer to the question)

There are multiple ways to select the trucks that represent the whole lot from the eight weigh stations:

Firstly: Systematic sampling can be used. For example: All truck numbers can be arranged ascendingly. And then every fifth truck can be inspected. This would assure random selection and complete coverage of the entire lot of trucks. Next time may be every 7th truck is inspected.

Like this in every sampling trial different numbers can be used to ensure all the trucks are covered over a period of time

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Secondly: Cluster samplig Since there are 8 different stations, these serve to be th clusters.

In Sample I: Say 7th and 2nd stations are completely inspected

In Sample II : 5th and 6th Stations are inspected

Like wise in multiple trials, different stations are completely covered. This would ensure thorough checking of each station over a period of time.

Cluster sampling requires lesser resources and time.