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Sample size $n+1$, sample mean = $X_{bar}$ (size = n), sample deviation = $S$ (size=n) How can we calculated confidence interval with 95% confidence, containing $X_{(n+1)}$ ?

If $E(X)=μ$, then $CI$ for $μ$ is $X_{bar} - t*S \sqrt n$, $X_{bar} + t*S\sqrt n$ as far as I think. However, I don't know exact way to find $CI$ for $X_{(n+1)}...$

PiGuy314
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hyemin ju
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  • Please use MathJaX to typeset equations: https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference – Gary Nov 10 '21 at 14:28
  • Such an interval is usually refered to as a prediction interval rather than a confidence interval. A derivation of the correct interval can be found at: https://en.wikipedia.org/wiki/Prediction_interval#Unknown_mean,_unknown_variance assuming that we are working with a normal distribution. – Leander Tilsted Kristensen Nov 10 '21 at 15:27

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