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Math is not my strongest part, yet, so I will be very grateful for your help and for giving the answer in sort of "plain" English, meaning that it will be great if you don't go too deep into the rabbit hole using difficult terminology, as these distribution issues are truly difficult for me

__Question__:

Below I show formulas, whose meanings I would like to understand, i.e. to understand the logic of each part - why we do this or that computation, the logic, intuition and the the result. I will, of course, show how I read them, thus you will see what I don't understand (hopefully).

To compute the confidence interval using t-distribution we use the following formula:

__First the formulas and an example:__

**X ± t**

_{α/2}x [s / √n]where X is the mean, s is the sample standard deviation (as we don't know the population standard devitation), n is the population size

δ = s / √n is the formula for the standard error.

For example, find the 95 percent confidence interval:

X = 3%, s = 6%, n = 10

Then, 3% ± t

_{0.025}x [6% / √10], hence, as t

_{0.025}= 2.262 (I took that from the table), the interval is from 1.64 to 4.36

__Questions:__

1) What is the meaning and how to read the standard error part s / √n ?

What are we trying to do here? We take standard deviation and divide it by the square root of the size, and thus we "break" the standard deviation into √n to get the value of one that part. What does it give us? And also why the square root?

2) Upon finding that number, we multiply it by the value of t

_{0.025}found for the degree of freedom of n - 1, that is 9. What does this mean?

Thank you very much.