Question

Please criticize the following statement regarding the interpretation of a confidence interval:

Results for a 95% Confidence Interval for estimating the population mean: 74.1< Mean< 83.1

" After looking at the above results we can conclude that there is a 95% chance that the confidence interval contains the true mean of the population"

Is the above statement correct? Why? If it is not correct how can we re-state the conclusion in order to interpret correctly the above confidence interval?

Answer 1

Yes, the above statement is correct, because we are given a 95% confidence interval for the population mean and we can interpret as 95% chance or probability of founding or getting population mean is the given confidence interval. For the given confidence interval, we are 95% confident that the population mean will lies between 74.1 and 83.1. We constructed the confidence interval for the population mean based on the sample data by using sample mean, sample standard deviation, and sample size. We use particular confidence level during the construction of confidence interval. For this scenario we use 95% confidence level. The 95% confidence level indicate that we are 95% confident or there is a 95% possibility or chance or probability of population mean being lies between lower and upper limit of confidence interval.