7.5 : Interpretation of Confidence Intervals

A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.

Confidence intervals have confidence coefficients that are crucial for their interpretation. The most common confidence coefficients are 0.90, 0.95, and 0.99, which can be written as percentages–90%, 95%, and 99%, respectively.

Suppose a person calculates a confidence interval with a confidence coefficient of 0.95. In that case, they can interpret that there is a 95% chance that the true value of the population parameter will fall in the calculated confidence interval. However, this may be incorrect, as the confidence interval is constructed from only one sample. Also, the population parameter is a fixed value and may or may not lie in the calculated confidence interval.

When a confidence coefficient of 95% is used, it means that from the multiple confidence intervals obtained after using identical sampling methods, 95% of them will contain the actual value of the population parameter. Further, in terms of statistical significance, it means that the many confidence intervals are not statistically different from each other and from the point estimate at a 0.05 significance level.