A sample of n = 16 scores has a mean of M = 83 and a standard deviation of s = 1

Question

A sample of n = 16 scores has a mean of M = 83 and a standard deviation of s = 12. a) Explain what is measured by the sample standard deviation. b) Compute the estimated standard error for the sample mean and explain what is measured by the standard error.
A sample of n = 16 scores has a mean of M = 83 and a standard deviation of s = 12. a) Explain what is measured by the sample standard deviation. b) Compute the estimated standard error for the sample mean and explain what is measured by the standard error.

Explanation / Answer

A) the sample standard deviation is a point estimate of the population standard deviation.

B) The standard error is /n = 12/16 = 12/4 = 3

The standard error is the standard deviation of the sampling distribution.

Another way to say it is that the standard error is the standard deviation of the distribution of sample means.

If you take a bunch of samples of the same size from the same populaion, these samples form their own distribution that is always approximately normal if you have enough samples. This distribution has its own standard deviation and it is called the standard error.

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