Calculator Inputs
Example Data Table
| Case | Method | Inputs | 90% Result |
|---|---|---|---|
| Mean example | Known standard deviation | n = 64, mean = 128, sigma = 12 | 125.5327 to 130.4673 |
| Sample mean example | Sample standard deviation | n = 25, mean = 73.6, s = 8.4 | 70.7257 to 76.4743 |
| Proportion example | Wilson interval | n = 200, successes = 126 | 0.5725 to 0.6841 |
Formula Used
For a mean with known standard deviation, use x̄ ± z × σ / √n.
For a mean with sample standard deviation, use x̄ ± t × s / √n.
For a Wald proportion interval, use p̂ ± z × √(p̂(1 - p̂) / n).
For a Wilson interval, use (p̂ + z² / 2n) / (1 + z² / n) ± adjusted margin.
For a two-sided 90% interval, the calculator uses the 95th percentile critical value. For one-sided limits, it uses the 90th percentile critical value.
When population size is entered, mean and Wald calculations may use √((N - n) / (N - 1)) as a finite population correction.
How To Use This Calculator
- Select the calculation method that matches your data.
- Choose two-sided, lower one-sided, or upper one-sided output.
- Enter the sample size and the required estimate fields.
- Add population size only when sampling without replacement.
- Pick the number of decimal places for the report.
- Press the calculate button and review the result above the form.
- Download the result as a CSV or PDF file.
90 Confidence Limit Guide
90 Confidence Limit Overview
A 90 confidence limit gives a practical range around an estimate. It shows where a population value may sit, using sample evidence. This calculator helps with means and proportions. It supports known standard deviation, sample standard deviation, Wald proportion limits, and Wilson proportion limits. Each choice fits a different data situation. The result is not a promise. It is a statistical interval built from assumptions.
Why Use This Calculator
Manual confidence work can be slow. Small typing errors can change the final range. This tool keeps the process organized. It separates the point estimate, standard error, critical value, margin of error, and final limits. That layout helps students, analysts, and researchers check their steps. It also makes reports easier to explain. You can round results to match your assignment or table format.
Best Data Inputs
Use the sample mean when measuring continuous values. Examples include weight, time, length, pressure, or cost. Enter a population standard deviation only when it is truly known. Otherwise, use the sample standard deviation option. Use the proportion tools when counting successes from trials. Examples include survey approval, defect rate, conversion rate, or pass rate. Wilson limits are often better for small samples or extreme proportions.
Reading The Results
The lower limit is the smaller plausible value. The upper limit is the larger plausible value. The margin of error is half the distance between those limits for symmetric mean intervals. For Wilson intervals, the shape can be slightly different. The standard error measures sample uncertainty. Larger samples usually reduce it. More variation usually increases it. A narrow interval suggests more precise estimation.
Important Notes
A 90 percent interval is narrower than a 95 percent interval. It accepts more risk of missing the true value. Always match the confidence level to the study plan. Check independence before trusting the answer. Random sampling matters. Outliers can affect mean intervals. Very small samples need careful review. Proportion results can be clamped between zero and one. Use exported files to keep records. When sharing results, include the method name. Include sample size and units. Mention whether the standard deviation was known or estimated. That context prevents confusion. Keep assumptions visible beside every reported confidence limit today.
FAQs
What is a 90 confidence limit?
It is a statistical boundary built from sample data. It estimates where a population value may reasonably fall when using a 90 percent confidence level.
When should I use the known standard deviation method?
Use it only when the population standard deviation is truly known. This is common in controlled processes, historical monitoring, or textbook problems.
When should I use the sample standard deviation method?
Use it when the population standard deviation is unknown. The calculator then uses degrees of freedom and a t critical value.
What is the Wilson proportion method?
Wilson is a proportion interval method. It often performs better than Wald when samples are small or proportions are near zero or one.
Can I enter a percent instead of a decimal?
Yes. Choose the percent scale before entering the proportion. You can also enter successes and sample size instead.
Why is one side shown as open?
A one-sided confidence limit gives only one boundary. A lower limit has no closed upper boundary, and an upper limit has no closed lower boundary.
What does finite population correction mean?
It adjusts the standard error when sampling without replacement from a limited population. Use it only when population size is meaningful.
Can I export the result?
Yes. After calculation, use the CSV or PDF buttons. They save the main result table for records, reports, or assignments.