Type-II Error Calculator

The App is a simple Type-II error calculator for the two-sided know variance case. This is pretty simple. The app calculates the probability of not rejecting H_0 in the case it is false. This can be seen in next page plot.
Type-II error is the blue area.
Type-II error is also know as beta.

This works by calculating the probability of seeing a x_bar under the real populations distribution.
For example,

• Imagine an observed x_bar = 4 with n = 10.
  
• Also, the population real variance is known. Sigma² = 0.5.
  
• Additionally, we know that the population real mean is 3.
  
• The test was done with an alpha = 0.05.
  
• What is type-II error?

#First calculate the mean standard error
n <- 10; sigma <- sqrt(0.5); std_e <- sigma/sqrt(n)

#Calculate bounds for non-rejection of null hypotesis
alpha <- 0.05; mu0 <- 4; mu <- 3; I <- c(alpha/2, 1 - alpha/2)
q <- qnorm(I, mean = mu0, sd = std_e)

#Calculate probabilities of type two error
b1 <- pnorm(q[1], mu, sigma); b2 <- pnorm(q[2], mu, sigma)
b <- b2 - b1
b

[1] 0.1925005