Suppose that many large samples are taken from a population whose data values have a standard deviation of 112.34. Which of the following could be the standard deviation of sample means?

Question

kj4uts · Answer

attachment

kropot72 · Answer

Consider the following:
The Standard Deviation of the sample means is given by
$$\large \frac{\sigma}{\sqrt{n}}$$
where sigma is the Standard Deviation of the population and n is the sample size.
Can you now see the correct choice of answer?

kropot72 · Answer

Yes, that is the Standard Deviation of the population. But keep in mind that the question is asking which of the choices is a POSSIBLE value for the standard deviation of sample means. The value of n is not given, but we know that the value of n is much greater than one. Therefore three of the answer choices cannot be correct.

kropot72 · Answer

If the standard deviation of sample means was 7.48, we would have:
$$\large \frac{112.34}{\sqrt{n}}=7.48$$
and the sample size n is given by:
$$\large n=(\frac{112.34}{7.48})^{2}=226$$
If you calculated the values of n using the other choices of answer, the values would all be lees than one.

kropot72 · Answer

less than one*

kj4uts · Answer

Yes, I tried them and got less than one.

kj4uts · Answer

so does that mean that 7.48 is the answer?

kropot72 · Answer

That is correct. The question states "many large samples are taken", therefore the only correct choice of answer must be a value of standard deviation of sample means which results in a value of n that is much greater than one.

kj4uts · Answer

Thank you very much for your help and time :)

kropot72 · Answer

You're welcome :)