Find the confidence interval for a mean. Enter your summary statistics, or paste the raw numbers, to get the interval, the margin of error, the critical value, and the standard error, then read what each one means.
Separate values with commas, spaces, or new lines. The mean, standard deviation, and n are computed from what you paste.
A confidence interval is a range of plausible values for a population mean, built from a single sample. Instead of reporting one point estimate, you report the estimate with a band around it that reflects how much sampling error you expect. The interval is the sample mean plus or minus the margin of error.
The confidence level describes the method over the long run, not the one interval in front of you. A 95 percent confidence interval means that if you repeated the study many times and built an interval each time, about 95 percent of those intervals would contain the true mean. It is tempting, but wrong, to say there is a 95 percent probability that the true mean lies inside this particular interval. The true mean is a fixed number, so for any single interval it is either inside or outside, and the 95 percent belongs to the procedure, not to one result.
The critical value scales the standard error into the margin of error. Use the t value when you estimate the standard deviation from your sample, which covers almost every real assignment. Use the z value only when the population standard deviation is genuinely known, which is rare outside textbook problems. The t value depends on the degrees of freedom, n minus one, and it is always a little wider than z to account for the extra uncertainty of estimating the standard deviation. With a large sample the two nearly agree, so when in doubt, keep the t value.
The margin of error is the critical value multiplied by the standard error, and the standard error is the standard deviation divided by the square root of n. Three things move the width of the interval: a larger sample narrows it, a larger standard deviation widens it, and a higher confidence level widens it. That last point is a trade-off, since more confidence costs precision. Ninety-five percent is the usual compromise.
This tool gives the correct interval for a single mean, but a graded assignment often asks for more: checking that the data are roughly normal or the sample is large enough, comparing groups, or building intervals for a proportion, a difference, or a regression coefficient. Our guide on how to interpret SPSS output walks through reading the interval off your tables, and a statistician can run and write up your analysis end to end.
Send your data and a statistician computes the interval, checks the assumptions, and writes the results section before your deadline.
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