This video shows the "by hand calculation" for constructing a confidence interval for a population proportion - and also illustrates the TI calculator method.
Constructing a confidence interval for a population mean when we "know" the population standard deviation is somewhat of a silly task - why would we know the population standard deviation and not know the population mean? Well, maybe we have some prior studies that give us some information about what the population standard deviation might be.
This technique is sort of unrealistic but is offered merely as a way to show you how it is done because the process for constructing confidence intervals when the population standard deviation is unknown is very similar. So, watch this video for the sake of completeness, but understand that in reality we would employ the Student t distribution for a confidence interval for a mean - covered in a subsequent video below!
This first video sets up the problem and shows how to read a t table to find the critical values and how to determine the lower and upper confidence limits using the formula.
It is really simple when you use a calculator function to construct a confidence interval - so focus on interpreting the interval - what does a 95% confidence interval for a mean tell you?