What does a 95% confidence interval actually mean?
It comes from a procedure that, if repeated on many samples, would capture the true parameter in about 95% of them. It does not mean there is a 95% probability that this one interval contains the truth.
Explain it simply
Imagine a net thrown at a fixed fish. The fish (true mean) does not move; the net (interval) lands in a different place for each sample. A 95% net catches the fish in 95 of 100 throws. Once one net has landed, the fish is either in it or not.
For a mean with a large enough sample: estimate +/- 1.96 x SE.
Example
A sample of 100 students shows a mean daily study time of 50 minutes with SD 10 minutes.
- SE = 10 / sqrt(100) = 1
- 95% CI = 50 +/- 1.96 x 1 = 48.04 to 51.96
mean, sd, n = 50, 10, 100
se = sd / n ** 0.5
print(round(mean - 1.96 * se, 2), round(mean + 1.96 * se, 2)) # 48.04 51.96A wider interval comes from higher confidence (99%), higher variability or a smaller sample. A narrower one needs more data.
What to say in the interview
"A 95% CI means that the method produces intervals that contain the true value 95% of the time over repeated sampling. It gives a plausible range for the parameter and the precision of my estimate. I avoid saying there is a 95% chance the true value is in this specific interval."
Common mistakes
- Reading it as the range containing 95% of the data. That would be a prediction or reference interval.