ZTest Class

The term Z-test is often used to refer specifically to the one-sample location test comparing the mean of a set of measurements to a given constant. Due to the central limit theorem, many test statistics are approximately normally distributed for large samples. Therefore, many statistical tests can be performed as approximate Z-tests if the sample size is large.

If the test is Significant, the null hypothesis can be rejected in favor of the alternate hypothesis specified at the creation of the test.

This test supports creating power analyses through its Analysis property.

References:

• Wikipedia, The Free Encyclopedia. Z-Test. Available on: http://en.wikipedia.org/wiki/Z-test

This example has been gathered from the Wikipedia's page about the Z-Test, available from: http://en.wikipedia.org/wiki/Z-test

Suppose there is a text comprehension test being run across a given demographic region. The mean score of the population from this entire region are around 100 points, with a standard deviation of 12 points.

There is a local school, however, whose 55 students attained an average score in the test of only about 96 points. Would their scores be surprisingly that low, or could this event have happened due to chance?

// So we would like to check that a sample of
// 55 students with a mean score of 96 points:

int sampleSize = 55;
double sampleMean = 96;

// Was expected to have happened by chance in a population with
// an hypothesized mean of 100 points and standard deviation of
// about 12 points:

double standardDeviation = 12;
double hypothesizedMean = 100;


// So we start by creating the test:
ZTest test = new ZTest(sampleMean, standardDeviation, sampleSize,
    hypothesizedMean, OneSampleHypothesis.ValueIsSmallerThanHypothesis);

// Now, we can check whether this result would be
// unlikely under a standard significance level:

bool significant  = test.Significant;

// We can also check the test statistic and its P-Value
double statistic = test.Statistic;
double pvalue = test.PValue;

Reference