The standard deviation of a sample of size 50 is 6.3. Determine the standard error whose population standard d

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Q. The standard deviation of a sample of size 50 is 6.3. Determine the standard error whose population standard deviation is 6.

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Standard error of the mean $=\sigma/\sqrt{n}=6/\sqrt{50}\approx 0.85$ .

When the population standard deviation $\sigma$ is known, the standard error of the sample mean is

$\text{S.E.}=\frac{\sigma}{\sqrt{n}}.$

Here $\sigma=6$ and $n=50$ , so

$\text{S.E.}=\frac{6}{\sqrt{50}}=\frac{6}{7.0711}\approx 0.8485.$ …

Q.The standard deviation of a sample of size 50 is 6.3. Determine the standard error whose population standard deviation is 6.