Available Confidence Intervals Calculators
- Two-Sided Difference of Proportions Test Calculator
- One-Sided Difference of Proportions Test
- T-Confidence Interval Calculator
- Normal Confidence Interval Calculator
A confidence interval function estimates a range of values that likely contains the true population value. It’s a tool used in statistics to measure uncertainty and to estimate parameters like the mean of a population.
How it works
- Calculate the sample mean
- Calculate the standard deviation
- Calculate the standard error
- Calculate the margin of error
- Plug the values into the formula for the confidence interval
- Interpret the results
The confidence interval is the range of values that likely contains the population mean. The width of the interval depends on the desired confidence level and the precision of the estimate.
Steps for calculating a confidence interval:
- Choose a confidence level, such as 95%
- Determine the Z-value for the chosen confidence level
- Calculate the margin of error
- Add and subtract the margin of error from the sample mean
Using a t-distribution
If the sample size is small (n ≤ 30), you can use the t-distribution instead of the z-distribution. The t-distribution is similar to the z-distribution, but corrects for small sample sizes.
Confidence interval purpose
Confidence intervals are used to estimate population parameters, such as the mean. They are a way to represent how “good” an estimate is.
Confidence level
The confidence level is the probability that the true value falls within the interval. For example, a 95% confidence interval means that 95% of the time, the true value will be within the interval.
Uses
Confidence intervals are used in hypothesis testing, regression analysis, and meta-analysis. They can also help determine if a difference is statistically significant.
Reporting
Confidence intervals are often reported with brackets around the upper and lower limits. For example, “95% CI [4.32, 7.26]”.