**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:

## 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.

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