Question

Suppose I have a population with μ = 25 and σ2=16. I take 10 samples of size 40.
a. What would be your best guess for the value of each of the sample means? (0.25 point)

Answer 1

Please show work as well.

Answer 2

im sure theres a formula that can go along with this ....

Answer 3

http://www.stat.yale.edu/Courses/1997-98/101/sampmn.htm

looks like theres someting in here that might be useful

Answer 4

I've already been to that website but I can't make sense of it.

Answer 5

is the a sigma^2? or a sigma_2?

Answer 6

it's to the second power

Answer 7

off hand id say my best guess of each sample mean is about 25 but i cant confirm that yet, still trying to read up on it

Answer 8

the formula with all our parts is:
\[\frac{\bar x -\mu}{\sigma/\sqrt{n}}\]
but im not sure what the "equals" to yes

Answer 9

*yet

Answer 10

well i just need to figure out how to calculate the independent random variables but I dunno how to do that.

Answer 11

the mean of the means is are the independant random variables in this case

Answer 12

zarkon is here tho so this might be easy for him :)

Answer 13

as amistre said....the best guess for each of the means (a point estimate) is 25

Answer 14

no formula needed

Answer 15

woohoo!!

Answer 16

I'm curious as to how to calculate the independent random variables exactly

Answer 17

using the central limit thrms formula that is an adaptation of the regular z= stuff id assume

Answer 18

?

Answer 19

recall:\[z=\frac{x-\mu}{\sigma} \]

Answer 20

in this case we have to "adjust" the sigma for some reason i cant remember to get:\[z=\frac{\bar x -\mu}{\sigma/\sqrt{n}}\]

Answer 21

spose you take a sample that has a mean of 33; how close would this be to the actual mean?

33-25
-------- = test statistic (zscore)
4/sqrt{40}