hw-9

Homework 9 in STAT400: Computational Statistics @ CSU

Assignment

Be sure to set.seed(400) at the beginning of your homework.

  1. Use the Monte Carlo simulation to investigate whether the empirical Type I error rate of the \(t\)-test is approximately equal to the nominal significance level when the sampled population is non-normal.

    1. For \(n = 5, 10, 30, 100, 500, 1000\), investigate the empirical type I error for a test of \(H_0: \mu = 1\) vs. \(H_a: \mu \not= 1\) when \(X_1, \dots, X_n \sim \chi^2(1)\) with \(m = 2000\) Monte Carlo samples with nominal \(\alpha = .05\).

    2. For \(n = 5, 10, 30, 100, 500, 1000\), investigate the empirical type I error for a test of \(H_0: \mu = 1\) vs. \(H_a: \mu \not= 1\) when \(X_1, \dots, X_n \sim Unif[0, 2]\) with \(m = 2000\) Monte Carlo samples with nominal \(\alpha = .05\).

    3. For \(n = 5, 10, 30, 100, 500, 1000\), investigate the empirical type I error for a test of \(H_0: \mu = 1\) vs. \(H_a: \mu \not= 1\) when \(X_1, \dots, X_n \sim Exponential(1)\) with \(m = 2000\) Monte Carlo samples with nominal \(\alpha = .05\).

    4. Compare your results in a.-c. in a table. What can you say about the departures from Normality as they relate to the Type I error rate of the \(t\)-test?

Turn in in a pdf of your homework to canvas. Your .Rmd file on rstudio.cloud will also be used in grading, so be sure they are identical and reproducible.