Class OneSampleZTest determines whether a sample from a normal distribution with known standard deviation could have a given mean. For example, suppose we wish to determine whether the IQs of children from a particular school are above average, given that Wechsler IQ scores are normally distributed with a mean of 100 and standard deviation of 15. Sample scores from 9 students are 116 110 111 113 112 113 111 109 121, with a mean of 112.8.
As described Section 6.1, all hypothesis test classes provide two paths for constructing instances of that type: a parameter-based method and a data-based method. Thus, you can construct a OneSampleZTest object by explicitly specifying a sample mean (
), sample size (
), population mean (
), and population standard deviation (
), like so:
double xbar = 112.8; int n = 9; double mu0 = 100; double sigma = 15; OneSampleZTest test = new OneSampleZTest( xbar, n, mu0, sigma );
Or by supplying a set of sample data, and the necessary population parameters:
DoubleVector data = new DoubleVector( "[ 116 110 111 113 112 113 111 109 121 ]" ); double mu0 = 100; double sigma = 15; OneSampleZTest test = new OneSampleZTest( data, mu0, sigma );
In this case, the sample mean and sample size are calculated from the given data.
In addition to the properties common to all hypothesis test objects (Section 6.1), a OneSampleZTest object provides the following read-only properties:
By default, a OneSampleZTest object performs a two-sided hypothesis test (
) with 
. In this example, we wish to test the one-sided form to the right (
; that is, we wish to test whether the children in our sample have a higher than average IQ. Suppose also that we wish to set the alpha level to 0.05. Non-default test parameters can be specified at the time of construction using constructor overloads, or after construction using the provided Alpha and Type properties, like so:
test.Type = HypothesisType.Right; test.Alpha = 0.05;
Once you've constructed and configured a OneSampleZTest object, you can access the test results using the provided properties, as described in Section 6.1:
Console.WriteLine( "z-statistic = " + test.Statistic ); Console.WriteLine( "p-value = " + test.P ); Console.WriteLine( "reject the null hypothesis? " + test.Reject);
z-statistic = 2.56 p-value = 0.00523360816355578 reject the null hypothesis? true
This indicates that we can reject the null hypotheses (
). We can conclude that the children have IQs significantly above average.
Finally, remember that the ToString() method returns a formatted string representation of the complete test results:
One Sample Z Test ----------------- Sample mean = 112.8 Sample size = 9 Population mean = 100 Population standard deviation = 15 Computed Z statistic: 2.56 Hypothesis type: one-sided to the right Null hypothesis: sample mean = population mean Alt hypothesis: sample mean > population mean P-value: 0.00523360816355578 REJECT the null hypothesis for alpha = 0.05 0.95 confidence interval: 104.575731865243 InfinityTOC | Previous | Next | Index