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Chapter 7: Problem 7

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 is more efficient, practical, less time-consuming, and less resource-intensive, while still providing valuable information about the entire population. This is why statisticians often analyze samples to make estimates or inferences about the population.

Step by step solution

01

Understand Populations and Samples

In statistical terms, a population encompasses every member of the set being studied. For instance, if you're interested in the lifetime of the batteries you're receiving, then your population is every single battery in that shipment. A sample, on the other hand, is a subset of that population, a few units chosen from the population to represent it.
02

Identify the Practicality of Studying the Entire Population

To examine each battery within your shipment would be very time-consuming and resource-intensive. If the shipment is large, it won't be practical to assess every battery's lifetime individually.
03

Understand the Purpose and Efficiency of Sampling

Sampling gives a high level of information about the population and can help in making inferences about the population like estimating means or testing hypotheses. By testing a sample, you can get a general idea of the entire population's attributes without needing to test every battery. It is practical, much less expensive, and efficient compared to testing the population.
04

Summarize the Importance of Sample in Statistics

So, an important aspect of statistics is that it allows us to make estimates or inferences about a population based on the data from a sample. It saves time, resources, and still provides valuable information of the whole population.

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Most popular questions from this chapter

In a die roll, 3 and 6 are multiples of 3 and \(1,2,4\), and 5 are not multiples of \(3 .\) Consider 90 rolls of a die on a random basis. a. From how many outcomes of the 90 rolls would you expect to get multiples of 3 , on average? b. If you actually counted, would you get exactly the number you predicted in part a? Explain.

Natural habitats must be protected to maintain the ecological balance. According to indexmundi.com's survey in 2010, about \(26 \%\) of the land in Brazil is a habitat-protected area. Suppose a geologist randomly selects 200 regions to study soil types found in the country. Use the Central Limit Theorem (and the Empirical Rule) to find the approximate probability that the proportion of protected regions is more than one standard error from the population value of \(0.26\). The conditions for using the Central Limit Theorem are satisfied because the sample is random; the population is more than 10 times \(1000 ; n\) times \(p\) is 52, and \(n\) times ( 1 minus \(p)\) is 148, and both are more than 10 .

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