Statistics HW Help: How to Calculate T-Distribution for Small Sample Sizes?

[lilyungn]

Homework Statement

I need help solving this problem:

Let A, B, C, D, and E are 6 units of a population. The measurements associated with A, B, C. D, E units are 76, 77, 78, 81, and 82, respectively.

-Find the population mean and its standard deviation

-List all possible samples of size 3 from those 5 units

-From each sample, compute the mean, standard deviation, and 95% confidence interval. Use t-distribution to estimate the tα/2 because we have a small size.

-How many intervals contain population mean? Can you verify your result with empirical rule? Do they agree?

Homework Equations

The Attempt at a Solution

I know the mean is 78.8 and standard deviation is 2.58844

 

[lilyungn]

I have solved out everything, I just need help to know how I get the t-distribution?