1
$\begingroup$

Working on notes in my Elementary Statistics course, I am trying to figure out why the standard deviation for a single sample used the standard deviation of the sample means. An example of what I am referring to is:

"A random sample size of 36 is taken from a population with mean µ = 17 and standard deviation σ = 6. What is the probability that the sample mean is greater than 18?"

The process being finding the z-score and using a standard normal distribution with $z = \frac{18-17}{6/\sqrt{36}}$

I understand that the standard deviation of all samples of size n is $\sigma_\bar{x} = \frac{\sigma}{\sqrt{n}}$. What I don't get is, why are we using $\sigma_\bar{x}$ for the standard deviation of that specific sample, when it is the standard deviation of all the sample means?

Improve this question
$\endgroup$

1 Answer 1

Reset to default
2
$\begingroup$

"A random sample size of 36 [...] What is the probability that the sample mean is greater than 18?"

You are NOT inferring information about a single sample: you are inferring information about the sample mean, so you use the dispersion of the sample means, which depends on the population parameters and also on the sample size.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.