Interpretation of Confidence Intervals

The confidence interval provides a reliable estimate of the population parameter that could be straightforward to calculate but often difficult to interpret.

Suppose we calculate the confidence interval at a 95% level. One may conclude that there is a 95% chance to find the true population parameter value within the calculated interval or a 95% probability that the calculated sample parameter value matches the true population parameter value.

This could be wrong, as the confidence limits calculated here are drawn from a single sample, which makes it unreliable.

Also, the true value of the population parameter is fixed, which may lie within or outside these limits.

A confidence interval at a 95% level means that if we obtain many confidence intervals using an identical sampling method, 95% of them would contain the true value of the population parameter.

In terms of statistical significance, it means that when the confidence interval is calculated at the 95% level, the confidence interval values are not statistically significantly different from each other and from the point estimate at 0.05.