public static TestResult ZTest( this IReadOnlyCollection<double> sample, double referenceMean, double referenceStandardDeviation )
<ExtensionAttribute> Public Shared Function ZTest ( sample As IReadOnlyCollection(Of Double), referenceMean As Double, referenceStandardDeviation As Double ) As TestResult
public: [ExtensionAttribute] static TestResult^ ZTest( IReadOnlyCollection<double>^ sample, double referenceMean, double referenceStandardDeviation )
[<ExtensionAttribute>] static member ZTest : sample : IReadOnlyCollection<float> * referenceMean : float * referenceStandardDeviation : float -> TestResult
A z-test determines whether the sample is compatible with a normal population with known mean and standard deviation. In most cases, Student's t-test (StudentTTest(IReadOnlyCollectionDouble, Double)), which does not assume a known population standard deviation, is more appropriate.
Suppose a standardized test exists, for which it is known that the mean score is 100 and the standard deviation is 15 across the entire population. The test is administered to a small sample of a subpopulation, who obtain a mean sample score of 95. You can use the z-test to determine how likely it is that the subpopulation mean really is lower than the population mean, that is that their slightly lower mean score in your sample is not merely a fluke.