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?
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$\begingroup$ Your question would be more clear if you have a specific example. $\endgroup$– RemyFeb 26, 2018 at 5:25
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$\begingroup$ 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 SFeb 26, 2018 at 5:28
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1 Answer
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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
$$\bar{X}=\frac{x+y}{2}$$
Can you go from here to solve for $s$?
