how to perform a ztest in matlab

To perform a z-test in MATLAB, you first need to calculate the z-score of your sample. The z-score is a measure of how many standard deviations your sample mean is away from the population mean:

main.m
zscore = (sample_mean - population_mean) / (population_std / sqrt(sample_size));
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Once you have the z-score, you can use the normcdf function to calculate the p-value:

main.m
pvalue = 1 - normcdf(abs(zscore));
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If the p-value is less than your chosen significance level (e.g. 0.05), you can reject the null hypothesis that the sample comes from a population with a certain mean.

For instance, let's say you want to perform a one-sample z-test to determine if a sample of 100 measurements of a certain variable with a mean of 4.2 comes from a population with a mean of 4. You define the significance level as 0.05. You can perform the z-test as follows:

main.m
% Define the input parameters
sample_mean = 4.2;
population_mean = 4;
population_std = 1;
sample_size = 100;
alpha = 0.05;

% Calculate the z-score and the p-value
zscore = (sample_mean - population_mean) / (population_std / sqrt(sample_size));
pvalue = 1 - normcdf(abs(zscore));

% Test whether the null hypothesis can be rejected
if pvalue < alpha
    fprintf('The null hypothesis can be rejected at the %g%% significance level.\n', alpha * 100);
else
    fprintf('The null hypothesis cannot be rejected at the %g%% significance level.\n', alpha * 100);
end
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This will output:

main.m
The null hypothesis can be rejected at the 5% significance level.
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