True / False: A population is always smaller than a sample.

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BlackTom AI · Accepted Answer

Question restatement: The statement asserts that a population is always smaller than a sample. Answer options are: 1) True 2) False

Option 1: True. This claim is inaccurate because, by definition in statistics, a sample is a subset of the population. The sample cannot be larger than the population it comes from. Therefore, it is incorrect to say the population is always smaller than a sample.

Option 2: False. This option correctly challenges the statement. Since a sample is drawn from the population, the population contains all elements from which the sample is drawn, and the sample size cannot exceed the population size. In typical scenarios, the population is equal to or larger than the sample, never smaller. This makes the assertion in Option 2 true about why Option 1 is wrong.

Additional nuance: Some contexts involve a sample being a full census of the population, in which case the sample size equals the population size. Even then, the population is not smaller than the sample; they are equal in size, not smaller. Therefore, the original statement misconstrues the relationship between population and sample.

Concepts involved: understanding the relationship between population and sample; recognizing that a sample is a subset (or census) of the population, which constrains sample size to be less than or equal to population size; and distinguishing between a false claim (population smaller than sample) and a true correction (population is not smaller than the sample).

STP420 - Probability and Statistics STP420 - Module 1 - Quiz STP420 - Probability and Statistics STP420 - Module 1 - Quiz

True / False: A population is always smaller than a sample.

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