Question

It’s possible to automatise this (using a loop, a function or something)? Currently I’m doing all the work “manually” (in other words, step by step), and it’s very annoying for me. I use kstest().

Consider the null hypothesis H0 : X ∼ N(0, 1).

For different values of µ (for instance µ = 0, 0.25, 0.50, 0.75, 1,) and for different values of n (for instance n = 25, 50, 100), do the following steps:

• Generate 1000 samples from N(µ, 1).
• For each sample, test the hypothesis H0 : X ∼ N(0, 1).
• Obtain the frequency of rejections in each case.
• Check that the level is well approximated when the null hypothesis is true
  (example, take α = 0.10, 0.05, 0.01).

Thank you so much.

Answer 1

I wrote a function to get the proportion of number for accepting null hypothesis, when you input the $\mu$, n and $\alpha$:

library(stats)
anxo <- function(mu, n, alpha){
  prop <- 0
  for (i in 1:n) {
     x <- rnorm(1000, mu, 1)
     if (ks.test(x, pnorm)$p.value > alpha) {
     prop <- prop + 1
     }
  }
  return(prop/n)
}