A friend of mine asked me to code the following in R: Generate samples of size 10 from Normal distribution with $\mu$ = 3 and $\sigma^2$ = 5; Compute the $\bar{x}$ and $\bar{x}\mp z_{\alpha/2}\displaystyle\frac{\sigma}{\sqrt{n}}$ using the 95% confidence level; Repeat the process 100 times; then Compute the percentage of the confidence intervals containing the true mean. So here is what I got, Staying with the default values, one would obtain The output is a list of Matrix and Decision , wherein the first column of the first list ( Matrix ) is the computed $\bar{x}$; the second and third columns are the lower and upper limits of the confidence interval, respectively; and the fourth column, is an array of ones -- if true mean is contained in the interval and zeros -- true mean not contained. Now how fast it would be if I were to code this in Python?
. . . a love story between theory and practice . . .