Estimations With Confidence

Estimations With Confidence

This site is a part of the JavaScript E-labs learning objects for decision making. Other JavaScript in this series are categorized under different areas of applications in the MENU section on this page.

Professor Hossein Arsham   


In practice, a confidence interval is used to express the uncertainty in a quantity being estimated. The following JavaScript that that computes confidence interval for standard deviation, confidence interval for variance, and confidence interval for expected value of the population based on a set of random observations. Since the Confidence Intervals (CI) are the duals of tests of hypothesis, one may use CI for testing too.

While the confidence interval for the mean is applicable to any population even with discrete random variables, such as proportion, the other two confidence intervals required testing for normality in order to be valid.

Let's say you compute a 95% confidence interval for a mean (or variance) of the population. The way to interpret this is to imagine an infinite number of samples from the same population, at least 95% of the computed intervals will contain the population mean (or variance), and at most 5% will not. However, it is wrong to state, "I am 95% confident that the population parameter falls within the interval."

Notice that care must be taken when rounding the confidence limits to a desirable number of digit the lower limit must be rounded up, while the upper limit must be rounded down. Know that a confidence interval computed from one sample will be different from a confidence interval computed from another sample.

One-sided Confidence Limits: To obtain the one sided (upper or lower) confidence interval with a level of significance, enter 1- 2a as the confidence level.

Test of Hypotheses by Confidence Interval: As an alternative to direct test of hypothesis for the Mean and the Variance one may use a two-sided or one-sided confidence interval to test a hypothesis with a two-sided or one sided alternative hypothesis , respectively. In this approach if the confidence interval with a desirable confidence level contains the null hypothesis value, then one might not reject the null hypothesis.

Enter your up-to-80 sample data, and the Desirable Confidence Level, and then click the Calculate button. Blank boxes are not included in the calculations but zeros are.

In entering your data to move from cell to cell in the data-matrix use the Tab key not arrow or enter keys.

To edit your data, including add/change/delete, you do not have to click on the "clear" button, and re-enter your data all over again. You may simply add a number to any blank cell, change a number to another in the same cell, or delete a number from a cell. After editing, then click the "calculate" button.

For extensive edit or to use the JavaScript for a new set of data, then use the "clear" button.


Enter a Confidence Level
Estimation of Mean with Confidence
Estimated Mean
Lower Limit
Upper Limit
Estimation of Variance with Confidence
Estimated Variance
Lower Limit
Upper Limit
Estimation of Standard Deviation with Confidence (for large samples, n>31)
Estimated Standard Deviation
Lower Limit
Upper Limit

For Technical Details, Back to:
Statistical Thinking for Decision Making


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Professor Hossein Arsham


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Kindly e-mail me your comments, suggestions, and concerns. Thank you.

Professor Hossein Arsham   


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