Resolved: why is the population mean, mu presented with sample mean here?
I was watching section 4, Confidence Intervals, and do not understand when talking about sample means that has been placed in the midpoint of the confidence interval, and at the same time 2.5% chance that the population mu is on the left and same on the right. Mu is used to represent population means, which means only 2.5% chance!!! And why it has to do with population when sample observation is made here?
The idea about working with a confidence interval is to consider a range that likely contains the true population mean.
So, for example if you're thinking about the average age of people in London and you don't know this true average age, then you might say: "Ok, I'm 99% certain that the average age of the population in this city is in the interval 20 years to 60 years". But this isn't very practical right? That range is too wide.
Because you want to improve your assessment and need to understand more about the average age in London, you interview people in that city and ask each person about their average age. 100 people tell you their age (your sample) and you calculate that the average of the 100 respondents is 35 years (sample mean).
You didn't interview the whole city and calculate their average age (which would have been the population mean).
Instead you use the information obtained from your sample (sample mean) to make inferences regarding the true population mean of the city of London.
This is one of the most important ideas in Statistics - we can make inferences about the true population mean by examining a portion of all observations and relying on the sample mean and the size of the sample we have worked with.
Hope this helps!