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 the server will also be used in grading, so be sure they are identical and reproducible.

Be sure to share your server project with the instructor and grader:

1. Open your hw-9 project on liberator.stat.colostate.edu

2. Click the drop down on the project (top right side) > Share Project…

   

3. Click the drop down and add “stat400instructors” to your project.

   

This is how you receive points for reproducibility on your homework!