Hey everyone! I'm having difficulty figuring out this question. It seems simple and straightforward enough, but I need some guidance as to what I need to do.
I know the x̄=51.25 and s = 4.367 and n = 8 but I don't understand how to find the confidence interval from this point on..Consider the sample 49 53 49 47 52 61 50 49 from a normal population with population mean μ and population variance σ^{2}. Find the 95% confidence interval for μ
The formula I'm given is:
x̄ ± z_{a/2} * (s/√n)
I know x̄ and s are, and I know a/2 = 0.05/2, the z-score that lines up with (0.5-[0.05/2]) is 1.96, but I don't know n, so how would I solve this?
any help appreciated!
EDIT: I also know that x̄ is representative of μ.
The answer key says the answer is 51.25 ± 3.65, but I don't understand where 3.65 came from.
I thought that too, so i decided to apply what you said to the next 4 exercises, and they're wrong as well. So then I'm guessing the way I calculated z_{a/2} is wrong, but I don't know any other possible logical way to get that number..
Awesome! Thanks a lot!
How exactly would you know if n is small or big? in this case, n = 8 but 8 being "small" or "big" is relative in terms of another number (i.e. 8 is bigger than 7, but 8 is smaller than 20). Is there a set rule as to how big n should be?