Confidence Intervals for Two Populations

Confidence Intervals for Two Populations

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   

The following JavaScript construct confidence intervals for difference in means (m1 - m2) and the ratio of variances (s12 / s22) for two populations, based on two sets of random observations and a desirable confidence level. 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 means is applicable to any unimodal population even with discrete random variables, such as proportion (provided there is sufficient observations), however, the confidence interval for variances required testing for normality in order to be valid.

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: Since the Confidence Intervals (CI) are the duals of tests of hypothesis, one may use CI for testing too. Therefore, as an alternative to direct test of hypothesis, 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 from the first population, and the second population in the following two tables, and a desirable confidence level.

Blank entry 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
Mean1 Mean2
Variance1 Variance2
Confidence Interval for Difference in Means
Confidence Interval for Variance Ratio

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

Kindly email your comments to:
Professor Hossein Arsham


Decision Tools in Economics & Finance

Probabilistic Modeling


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Professor Hossein Arsham   

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