What does a 95% confidence interval mean in statistics?

• A. The probability of including the true value within the range is 0.95.
• B. There is a 95% probability that the observed sample statistic lies within this interval.
• C. The interval will contain 95% of the population values.
• D. The interval indicates that 95% of the time the null hypothesis is true.

Answer: (A)

A 95% confidence interval expresses how confident we are in the interval produced from the data, given the method used. If we could repeat the study many times and construct a similar interval from each sample, about 95% of those intervals would contain the true value of the parameter. It’s about long-run performance of the interval under repeated sampling, not a guarantee about this single observed interval. For this specific interval, the true value is fixed, and the interval either contains it or it doesn’t; the 95% figure refers to the frequency with which the method would succeed across many repetitions. It does not mean that 95% of population values lie inside the interval, nor does it say anything about the probability that the null hypothesis is true.