# Thread: Finding the confidence interval from a sample of a normal population

1. ## Finding the confidence interval from a sample of a normal population

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.
Consider the sample 49 53 49 47 52 61 50 49 from a normal population with population mean μ and population variance σ2. Find the 95% confidence interval for μ
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..

The formula I'm given is:

x̄ ± za/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.

2. ## Re: Finding the confidence interval from a sample of a normal population

Originally Posted by snypeshow

The answer key says the answer is 51.25 ± 3.65, but I don't understand where 3.65 came from.
Try $1.96 \times \frac{4.367}{\sqrt{8}}$

3. ## Re: Finding the confidence interval from a sample of a normal population

that equals 3.026, the answer was 3.65

4. ## Re: Finding the confidence interval from a sample of a normal population

The answer key is sometimes wrong.

If this is for submission show your workings, this will show your assessor you have an understanding of the topic.

5. ## Re: Finding the confidence interval from a sample of a normal population

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 za/2 is wrong, but I don't know any other possible logical way to get that number..

6. ## Re: Finding the confidence interval from a sample of a normal population

Now as $\sigma$ is not known and $n$ is small, discard $Z_{\frac{\alpha}{2}}$ in favour of $t_{n-1,\frac{\alpha}{2}}$

7. ## Re: Finding the confidence interval from a sample of a normal population

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?

8. ## Re: Finding the confidence interval from a sample of a normal population

Rule of thumb, n=30 is large enough as data distribution can be observed by then.