Confidence Interval for Mean Calculator


Instructions: Use this step-by-step Confidence Interval for Mean Calculator, with known population variance, by providing the sample data in the form below:

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




Confidence Interval for Mean Calculator

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 \(\mu\). The confidence level is pre specified, and the higher the confidence level we desire, the wider the confidence interval will be. The following expression to compute the confidence interval for the mean is used:

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

where the critical value correspond to critical values associated to the Normal distribution. The critical values for the given \(\alpha\) is \(z_c = z_{1 - \alpha/2}\).

Assumptions that need to be met

For the case of the confidence interval for a population mean, you need the normality assumption met, which means that the sample is drawn from a normally distributed population. Also, in order to use the above formula we need to have that the population standard deviation is known.

Other Calculators you can use

In case the population standard deviation is not known, you can use this confidence interval calculator for a population means when the population standard deviation is not known. Also, if you are dealing with two population means, you can use this calculator for the confidence interval for the difference between means.




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