Statistics > Confidence Intervals > 1-Population Mean

This utility computes the confidence intervals for a population mean in one population, whether the population standard deviation is known or unknown. The confidence intervals are calculated using the following formulas:

where when population standard deviation is known
or when is unknown;
= sample mean
μ = population mean
s = sample standard deviation
= inverse cumulative probability of the Student's t distribution at 1 - α/2.
= inverse cumulative probability of the z distribution at 1 - α/2.

• If population standard deviation is known, select the Known radio button, and enter the standard deviation in the given text box. Otherwise, select the Unknown radio button.
• You can provide sample data in a column of the Datasheet or provide summary data. If your sample data is available in one column, select the Samples in column: radio button, and select the column name in the given drop-down menu.
• If individual sample data is not available, you can provide summary information of the sample data. In this case, select the Summarized sample data radio button. Enter the sample size, mean, and standard deviation (only if population standard deviation is unknown) in the provided text boxes.
• Enter the confidence level (between 0 and 1) in the Confidence level: text box.
• Click Ok to compute the confidence interval. The results will be shown in the log window.

The sample size, mean, and/or standard deviation are displayed along with the margin of error and the resulting confidence interval. Here is an example:

Confidence Interval - One population mean: confidence level = 0.95
Input: C1
σ known
Assumed population standard deviation σ = 2.0

N	Mean	Margin of Error	95.00%CI
5	2.080	1.753	(0.327, 3.833)