Suppose we are planning on taking a simple random sample from a population. If we double the sample size, then the standard deviation of the sample means will change by a factor of:Group of answer choices √ 21/ √ 2 21/ 2won't change at all
Question
Suppose we are planning on taking a simple random sample from a population. If we double the sample size, then the standard deviation of the sample means will change by a factor of:Group of answer choices √ 21/ √ 2 21/ 2won't change at all
Solution
The standard deviation of the sample means, also known as the standard error, is given by the formula:
Standard Error = σ/√n
where σ is the standard deviation of the population and n is the sample size.
If we double the sample size, the new standard error will be:
New Standard Error = σ/√(2n)
To find the factor by which the standard error changes, we can divide the new standard error by the old standard error:
Factor = (σ/√(2n)) / (σ/√n) = √n / √(2n) = 1/√2
So, if we double the sample size, the standard deviation of the sample means will change by a factor of 1/√2. Therefore, the correct answer is 1/ √ 2.
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