How to find the sample mean and sample standard deviation if only given the $n$ sample size and that the sample $95%$ confidence interval is $(x, y)$? If I was given one of them I would know how to find the other one, but what should I do if both of them are unknown?

  • $\begingroup$ Your question would be more clear if you have a specific example. $\endgroup$ – Remy Feb 26 '18 at 5:25
  • $\begingroup$ Sure, the question says "Using a sample of size n=100, a paper reported a large sample 95% confidence interval for the true mean of a population to be (3:7552;5:2448). What were the sample mean and sample standard deviation?" $\endgroup$ – George S Feb 26 '18 at 5:28

A $95$% confidence interval is given by

$$\bar{X} \pm 1.96 \frac{s}{\sqrt{n}}$$

where $n=100$

If your confidence interval is $(x,y)$ then


Can you go from here to solve for $s$?

  • 1
    $\begingroup$ Thank you very much, that's more than clear $\endgroup$ – George S Feb 26 '18 at 5:31
  • 1
    $\begingroup$ Yes, I just didn't know that we can get the sample mean that way $\endgroup$ – George S Feb 26 '18 at 5:31

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