Find a confidence interval for a mean from the sample mean, standard deviation, and size. Enter the statistics and pick the confidence.
Usage Tip
A wider interval means more confidence but less precision; a larger sample narrows the interval.
z from the confidence level
At 95 percent confidence, 95 percent of such intervals would capture the true mean.
This uses the normal (z) approximation, best for larger samples.
The margin is z times the standard error.
A confidence interval gives a range around the sample mean that is likely to contain the true population mean. The width of the interval is the margin of error, and it depends on the standard deviation, the sample size, and the confidence level you choose. A larger sample narrows the interval, while a higher confidence level widens it.
A 95 percent interval does not mean there is a 95 percent chance that the true mean lies in this particular range. It means that if you repeated the sampling many times, about 95 percent of the intervals built this way would contain the true mean. For small samples where the population standard deviation is unknown, an interval based on the t distribution is more appropriate than one based on the normal distribution.