In a 95% Confidence Interval, the true mean has what chance of falling between the Lower
Limit and Upper Limits of the calculated confidence interval?
In a 95% confidence interval, there is a 95% chance that the true mean falls between the lower limit and upper limit of the calculated interval. This means that if we were to repeat the sampling process many times and construct a confidence interval for each sample, we would expect that about 95% of those intervals would contain the true population mean.
To calculate a 95% confidence interval, you typically need to know the sample mean, standard deviation, and sample size. The general formula for a confidence interval is:
Lower Limit = Sample Mean - (Z * (Sample Standard Deviation / √n))
Upper Limit = Sample Mean + (Z * (Sample Standard Deviation / √n))
Where:
- Sample Mean is the average value of your sample
- Z is the Z-score, which depends on the desired level of confidence (for 95% confidence, Z ≈ 1.96)
- Sample Standard Deviation is a measure of the spread of your sample data
- n is the sample size
By plugging in the appropriate values, you can calculate the lower and upper limits of the confidence interval. The true mean is expected to fall between these limits with a 95% probability.