Page 220 - Computational Statistics Handbook with MATLAB

Chapter 6: Monte Carlo Methods for Inferential Statistics 207

H : µ = 454
0
H 1 : µ < 454.

We will perform our hypothesis test using simulation to get the critical val-
ues. We decide to use the following as our test statistic

x – 454
z = ------------------ .
σ ⁄ n

First, we take care of some preliminaries.
% Load up the data.
load mcdata
n = length(mcdata);
% Population sigma is known.
sigma = 7.8;
sigxbar = sigma/sqrt(n);
% Get the observed value of the test statistic.
Tobs = (mean(mcdata)-454)/sigxbar;
The observed value of the test statistic is t o = – 2.56. The next step is to
decide on a model for the population that generated our data. We suspect
that the normal distribution with σ = 7.8 is a good model, and we check this
assumption using a normal probability plot. The resulting plot in Figure 6.4
shows that we can use the normal distribution as the pseudo-population.
% This command generates the normal probability plot.
% It is a function in the MATLAB Statistics Toolbox.
normplot(mcdata)
We are now ready to implement the Monte Carlo simulation. We use 1000 tri-
als in this example. At each trial, we randomly sample from the distribution
of the test statistic under the null hypothesis (the normal distribution with
µ = 454 and σ = 7.8 ) and record the value of the test statistic.
M = 1000;% Number of Monte Carlo trials
% Storage for test statistics from the MC trials.
Tm = zeros(1,M);
% Start the simulation.
for i = 1:M
% Generate a random sample under H_0
% where n is the sample size.
xs = sigma*randn(1,n) + 454;
Tm(i) = (mean(xs) - 454)/sigxbar;
end

© 2002 by Chapman & Hall/CRC