The task today is to implement hypothesis testing in MatLab.
A simple test of a normal mean should follow these steps:
Use this data of sample size n = 100 to perform the hypothesis test Ho: mu =< 4 vs. Ha: mu > 4, for alpha = 0.1. Then plot the power of the test as a function of the true population mean. Note that the population standard deviation is known to be 0.2. Use the following MatLab commands to do this.
% read in the data and call it something like "HT"
% first find the critical value since you already
% know the hypothesis and the alpha level
alpha = 0.1;
n=length(HT);
std = 0.2;
Za = norminv(1-alpha,0,1);
CV = 4 + Za*std/sqrt(n); % any test statistic greater than CV
% will lead to the rejection of the
% null hypothesis, since we have a right
% tailed test
% what is the test statistic we have from the sample?
tstat = mean(HT); % does this fall in the rejection region?
% what if you have alpha = 0.05 instead?
Now we will look at the power of the hypothesis test. Remember that the power of the test is one minus the probability of making a type II error. This depends on the true value of the population mean instead of the hypothesized mean, so we will consider a range of possible values under the alternative hypothesis.
MU = 4:0.001:4.1;
POWER = 1- normcdf((CV - MU)/std*sqrt(n),0,1); % what is going on here?
plot(MU,POWER); % plot true mean verses power of test for
% corresponding mean
xlabel('Mu');
ylabel('Power');
To see what is going on with the power of a hypothesis test take a look at this Java applet:
http://www.stat.sc.edu/~ogden/javahtml/power/power.html
If you understand this applet, then you should understand the type I, and type II errors, their probabilities, and power.