Question

State how you would respond to the following student posts in a discussion on how to interpret a 95% confidence interval for a population mean.

One student posted their interpretation as “There is a 95% chance that this population mean will fall inside the confidence interval.” Another student responded to this post with “I don’t think that your interpretation is correct. The population mean is a fixed value. There is no chance involved. The population mean either falls inside the confidence interval or it does not.”

Answer 1

Interpreation for 95% confidence interval is given as "The probability that the population mean would lie between the confidence intervavl is 0.95".

And it is a similar interpretaion of the first student. Based on the samples collected from the population, there is a 95% chance that the population mean would fall into the confidence interval.

As second students statement, population mean may be fixed value but since we are trying to estimate using the sample it is still a chance that the population mean.