[Solved] When Sampling Is Done Without Replacement Then Standard ...

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Standard Error:

  1. The standard error of the mean is the standard deviation of the sampling distribution of the mean.
  2. In other words, it is the standard deviation of a large number of sample means of the same sample size drawn from the same population.
  3. The term standard error of the mean is commonly (though imprecisely) shortened to just standard error.
  4. The "standard error of the mean" refers to the standard deviation of the distribution of sample means taken from a population.
  5. The smaller the standard error, the more representative the sample will be of the overall population.

quesImage56 In sampling without replacement, the formula for the standard deviation of all sample means for samples of size n must be modified by including a finite population correction. The formula becomes: where N is the population size.

Thus, option 2 is the correct answer.

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When sampling with replacement the standard deviation of all sample means equals the standard deviation of the population divided by the square root of the sample size when sampling with replacement.

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