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I am trying to create a 95% confidence interval for the differences between this data which i'm assuming comes from a normal distribution. I have been searching although im unsure if I'm using the correct formula. This is for work.

I have a mean, sd and n for data 1:

Mean1 = 10 Sd1 = 2 N1 = 130

And similarly for data 2:

Mean2 = 8 Sd2 = 2.5 N2=138

For the mean difference I was doing (130*10 - 8*138)/(130+138)

But how do I calculate the sd? I assume once I have this I can take the mean difference +/- new sd multiplied by 1.96 to get a confidence interval

JB191
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  • Why are you estimating the difference in this way? What exactly is the parameter you need a confidence interval for? – whuber Jan 16 '24 at 21:30
  • @whuber I've been asked to get the difference between the means and express the uncertainty around these values to measure the separation – JB191 Jan 16 '24 at 22:17
  • Okay. For more answers, please search our site. – whuber Jan 16 '24 at 22:59
  • @whuber but these questions do not help me, they are different – JB191 Jan 16 '24 at 23:12
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    They both ask your question: how to obtain a confidence interval for the difference of means of two normal distributions, independently sampled. – whuber Jan 16 '24 at 23:17
  • @JB191 While both are related, the second one in particular looked to me to be a very direct answer (albeit largely or partly covered in the question and in comments, not just in the answer section) to what you seem to be asking. If you are certain it doesn't cover what you want to know, you'd need to edit to clarify how your question is not asking what is discussed there. – Glen_b Jan 16 '24 at 23:33

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