My (basic) understanding of a 95% confidence interval is that it is the interval within which the sample mean would fall 95 times should you take 100 random samples from the population.
My query is this, I often see confidence intervals being used in situations that I would call descriptive, rather than inferential. Is this a proper and correct way of using them?
For instance, if I measure every single washer in my factory, and plot the mean with the 95% confidence interval, what am I saying? If I retake the 'sample' 100 times, I'll get the same mean 100 times. But I'd argue it's useful to have a confidence interval because it serves a descriptive function in terms of sample size and spread of the data.
Let's say I measure all the washers in my factory every month and want to use confidence intervals to see if there is a significant difference between the mean diameter between this month and the previous month. Is this concept flawed because I am looking at populations rather than samples? If I am 100% certain of the mean each month then do questions of significance cease to matter?
I'm aware this may be a stupid question, links to suitable reading material accepted gratefully!