Margin of error | ±0.7157 |
Confidence interval | (9.2843, 10.7157) |
Sample size | 30.00 |
Statistical inference is a powerful tool for making decisions based on sample data. This article explains how to use our point estimate calculator to generate confidence intervals for population parameters including means, proportions, variances, and standard deviations.
A point estimate is a single value that serves as the best guess for an unknown population parameter, based on sample data. While useful, point estimates don't tell us about precision or uncertainty. That's where confidence intervals come in.
A confidence interval provides a range of plausible values for the unknown population parameter, along with a confidence level (typically 90%, 95%, or 99%) that indicates how certain we can be that this interval contains the true parameter.
For example, a 95% confidence interval means that if we were to take many samples and construct confidence intervals from each sample, approximately 95% of these intervals would contain the true population parameter.
Our calculator offers four different options for calculating point estimates and confidence intervals:
Use this tab when you want to estimate a population mean.
Required inputs:
The calculator uses these formulas:
Where:
The confidence interval is then calculated as:
Where x̄ is the sample mean.
Use this tab when estimating a population proportion (percentage or probability).
Required inputs:
The calculator first determines the sample proportion:
Then calculates the margin of error:
The confidence interval is p̂ ± Margin of Error, with adjustments to ensure the interval stays within [0,1].
Use this tab when estimating a population variance.
Required inputs:
The calculator uses the chi-square distribution to compute the confidence interval:
Where:
Use this tab when estimating a population standard deviation.
Required inputs:
Similar to the variance calculation, but with square roots applied:
The calculator provides:
When interpreting confidence intervals, remember:
For valid results, be aware of these calculator assumptions:
By understanding point estimates and confidence intervals, you can make more informed decisions under uncertainty and better communicate the reliability of your statistical findings.