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Confidence intervals, which formula to use 
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#1
Mar1912, 11:37 AM

P: 21

I have created 1000 random samples of size 10, where X~N(8,2). For each sample I have calculated the sample mean, sample variance, (sigma_{1})^{2} and (sigma_{2})^{2}.
I want to find a 95% confidence interval for the mean assuming the population variance is known, and a 95% confidence interval for the mean assuming the population variance is unknown. What formula do I use for these? I think, given that I am sampling from a normal distribution, for the known confidence interval, would be: (X_{1}bar X_{2}bar) + z_{a/2}s.e.(X_{1}barX_{2}bar) given that the samples are sufficiently small enough. For unknown, I think it's: (X1bar X2bar) + t_{((n1+n22),a/2)} s.e(X_{1}barX_{2}bar) <<s.e has a tilda over it, also this formula assumes the sigmas are the same. Is this correct? 


#2
Mar1912, 12:18 PM

Sci Advisor
P: 3,313

(You should look at http://physicsforums.com/showthread.php?t=546968 instead of using the SUB tag.) Can you explain your objective in doing this calculation. As I understand your post, you already know the population mean and variance. So why are you seeking a confidence interval for it? Is this an experiment in testing the theory of confidence intervals? 


#3
Mar2012, 08:09 AM

P: 21

both sigmas have a hat on for estimated σ_{1}^{2} = [sum_{(from i=1 to n)}(x_{i}xbar)^{2}]/n σ_{2}^{2} = same but divided by n+1 (Will have a look at LaTeX, usually I get some of it to work and when it comes to summations and things I can't grasp it, which is weird as I'm quite good at coding in R, maple, etc) 


#4
Mar2012, 10:47 AM

Sci Advisor
P: 3,313

Confidence intervals, which formula to use
That clears up the definition of the sigmas, but your statement of the assignment is still incoherent. For an assigned problem, its best to obey the format of the homework section of the forum and state the exercise exactly as it was assigned. Can you do that? 


#5
Mar2012, 03:12 PM

P: 21

I can, but it's not homework, it is revision for exams, they are extra problems we can choose to do which will help us in exams.
The question is stated as it is, but instead of saying I wish to find, it says, find, I haven't left any information out, and have asked it in the first person instead. 


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