7.5:
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.
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.