Confidence Interval for Mean Calculator for Unknown Standard Deviation


Instructions: Use this step-by-step Confidence Interval for Mean Calculator, with unknown population variance, by providing the sample mean, sample standard deviation and sample size in the form below:

Sample Mean \((\bar X)\) =
Sample Standard Deviation \((s)\)
Sample Size \((N)\)
Confidence Level (Ex: 0.95, 95, 99, 99%) =



Confidence Interval for Mean Calculator for Unknown Population Standard Deviation

A confidence interval corresponds to a region in which we are fairly confident that a population parameter is contained by. The population parameter in this case is the population mean \(\mu\). You need to specify a certain confidence level, which will determine the width of the confidence interval. The following expression is used to compute the confidence interval for the mean:

\[ CI = \displaystyle \left(\bar X - t_c \times \frac{s}{\sqrt n}, \bar X + t_c \times \frac{s}{\sqrt n} \right) \]

where the critical value correspond to critical values associated to the t-distribution with \(df = n - 1\) degrees of freddom. The critical value for the given \(\alpha\) and \(df = n - 1\) is \(t_c = t_{1 - \alpha/2; n-1}\).

Assumptions that need to be met

As for most of the confidence intervals we have dealt with, this calculator require that the sample is drawn from a normally distributed population. In this case we don't need the population standard deviation \(\sigma\) to be known, and we can use instead the sample standard deviation \(s\).

Other Calculators you can use

In case the population standard deviation is known, you can use this confidence interval calculator for a population means when the population standard deviation is known.




In case you have any suggestion, or if you would like to report a broken solver/calculator, please do not hesitate to contact us.

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