Thread: [SOLVED] 2-sided confidence interval for small sample

33. degrees of polymerization are:
418 421 421 422 425 427 431

434 437 439 446 447 448 453

454 463 465

c. Calculate a two-sided 95% confidence interval for true average degree of polymerization.

n=17 (so I will calculate a t-confidence interval)
t-confidence interval= mean +/- (t-critical value * s/√n)

I have calculated ∑x=7,451 so ∑x²=55,517,401. So the mean is 7,451/17≈ 438.29. t-critical value is 2.11. √n=√17≈4.123.
If I understand this, then I just need to calculate s to attain the confidence interval. However, I don't know how to calculate s without having the probability of each x. (i.e. √σ=E(x²)-[E(x)]²).

Please let me know how my logic is failing and what I need to do to solve this problem. I have spend several hours on this.

Thanks a bunch!
-Yvonne

I found my answer:

s=√[(∑(x-mean))²/n-1)]
s=15.14


Hope this helps others.