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As the sample size increases, theGroup of answer choicespopulation mean increasesstandard deviation of the population decreasesstandard error of the mean decreasesstandard error of the mean increases

Question

As the sample size increases, theGroup of answer choicespopulation mean increasesstandard deviation of the population decreasesstandard error of the mean decreasesstandard error of the mean increases

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Solution

As the sample size increases, the standard error of the mean decreases.

Here's why:

  1. The standard error of the mean (SEM) is a measure of how spread out the means of different samples from the same population are likely to be. It is calculated as the standard deviation divided by the square root of the sample size.

  2. As the sample size increases, the denominator of this fraction (the square root of the sample size) gets larger.

  3. Because the standard deviation is divided by this larger number, the standard error of the mean becomes smaller.

  4. Therefore, as the sample size increases, the standard error of the mean decreases.

Note: The sample size has no effect on the population mean or the standard deviation of the population. These are characteristics of the population itself and do not change with the size of the sample taken from that population.

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