I generate 1,000 random samples from a posterior distribution which is $t_{19}(7.925, 0.14)$.
Now by using those 1000 samples, I'd like to estimate the 90% interval for $\mu$ (By the interval, I guess credible interval...).
Here are some information, you might find it helpful
(1).Interesting parameter is $\mu$.
(2).I have 20 randomly chosen samples $y_{1}=7, ...,y_{20}=5$
(3).Posterior distribution is $\mu|y\sim t_{19}(7.925, 0.14)$
(4).100(1-$\alpha$)% credible interval for $\mu$ is $\bar{y}\pm t_{n-1,\alpha/2}\,\large\frac{s}{\sqrt{n}} $
I thought I could just calculate the 90% interval by using (4) but then I realized that I have to do it with the ones I generated.... and I guess I got stuck here.
Can anyone give me some advice?
Thank you.