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Chapter 7: Problem 13

You are receiving a large shipment of batteries and want to test their lifetimes. Explain why you would want to test a sample of batteries rather than the entire population.

Short Answer

Expert verified
Testing a sample of batteries rather than the entire population can save time, cost, and resources while still providing a reasonably accurate estimate of the overall battery lifetime, considering the sample is representative of the population. It also avoids the impracticality of destructive testing of all the batteries.

Step by step solution

01

Understanding the Population and Sample Concept

The first step is to understand the main difference between a population and a sample. The population refers to the complete set of items鈥� in this case, all the batteries. A sample, however, is a subset of the population, like testing only a few batteries from the entire lot.
02

Reasons for Using Samples

Consider several reasons why one would opt to test a sample of batteries as opposed to the entire population. Here are some ideas: 1. Time constraint: Testing every battery can be incredibly time-consuming, especially with large shipments.2. Cost-effectiveness: Not every battery needs to be tested to get an accurate idea of the overall quality. Testing selected ones reduces costs.3. Practicality: Some tests may involve destructive processes (like running the battery until it dies), which would make the batteries unuseable afterwards.
03

Understanding the Statistical Representation

Finally, comprehend that if the sample is representative, meaning it fairly reflects the characteristics of the whole population, then testing a sample will give a good idea of the lifetime of the entire population of batteries. This is the basis of inferential statistics, where conclusions about a population are drawn from a smaller sample.

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