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The standard deviation of a sampled population is also called the standard error of the sample mean.Group of answer choicesTrueFalse

Question

The standard deviation of a sampled population is also called the standard error of the sample mean.

Group of answer choices

  • True
  • False
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Solution

Answer

The statement is True.

Explanation

The standard deviation of a sampled population is indeed referred to as the standard error of the sample mean (SEM) when calculating the dispersion of sample means. The SEM measures how much the sample mean is expected to fluctuate from the true population mean. It is calculated by dividing the standard deviation of the sample by the square root of the sample size (n):

SEM=sn \text{SEM} = \frac{s}{\sqrt{n}}

where ss is the standard deviation of the sample. Thus, in the context of sampling distributions, the standard deviation of a population does relate to the standard error of the sample mean.

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