A confidence interval reports an estimate together with its precision, instead of a single number that looks exact.
It answers how far the true population value might plausibly be from the estimate.
Narrow intervals mean a precise estimate, and wide intervals mean the data cannot pin the value down.
For large samples, a 95% interval for a mean is the estimate plus or minus about 1.96 standard errors.
The 1.96 comes from the normal distribution, where 95% of values lie within 1.96 standard deviations of the mean.
A 99% interval uses about 2.58 standard errors, so it is wider; more confidence costs precision.
For small samples the multiplier is a little larger than 1.96, to allow for the extra uncertainty.
Bigger samples shrink the interval, because they shrink the standard error.
Intervals for a difference between 2 groups are especially useful: if the interval excludes 0, chance alone is an unlikely explanation.
Only random error is covered, so a biased sample can give a narrow interval around the wrong value.
Overlapping intervals for 2 groups do not prove the groups are the same, since the difference needs its own interval.
The interval says nothing about where individual values fall, which needs the spread of the data instead.
In practice, reporting 30 minutes with a 95% interval of 28 to 32 tells readers far more than 30 minutes alone.
Decision makers often find intervals easier to use than a yes or no verdict, because they show the likely size of an effect.
The usual misreading is saying there is a 95% chance the true value lies in this interval, when the 95% belongs to the method.