Interpretation of 95% confidence interval.

Interpretation of 95% confidence interval.

• A. The interval within which 95% of sample estimates fall.
• B. The true population parameter lies within the interval with 95% probability.
• C. If the study were repeated many times, 95% of the calculated intervals would contain the true parameter.
• D. The probability that the null hypothesis is true is 95%.

Answer: (C)

A 95% confidence interval communicates how reliable our interval-building method is across repeated samples. It means that if we repeated the study many times and each time calculated a 95% interval in the same way, about 95% of those intervals would contain the true population parameter. In a single study, the parameter is fixed, so it either lies in this interval or it does not—probability doesn’t apply to the parameter itself, only to the long-run performance of the method. This interval is not saying that 95% of individual sample estimates fall inside it, nor does it speak to the probability that the null hypothesis is true. So the correct interpretation is about the long-run proportion of intervals that capture the true parameter.

A 95% confidence interval communicates how reliable our interval-building method is across repeated samples. It means that if we repeated the study many times and each time calculated a 95% interval in the same way, about 95% of those intervals would contain the true population parameter. In a single study, the parameter is fixed, so it either lies in this interval or it does not—probability doesn’t apply to the parameter itself, only to the long-run performance of the method. This interval is not saying that 95% of individual sample estimates fall inside it, nor does it speak to the probability that the null hypothesis is true. So the correct interpretation is about the long-run proportion of intervals that capture the true parameter.