zTest

zTest(X, [Y], [mu=0.0], [sigmaX=1.0], [sigmaY=1.0], [confLevel=0.95])

X is a numeric vector indicating the sample for the Z-test.

Y (optional) is a numeric vector indicating the second sample for a paired-sample Z-test. It is optional.

mu (optional) is a floating number. If Y is not specified, mu is the mean value of X in the null hypothesis; if Y is specified, mu is the difference in the mean values of X and Y in the null hypothesis. It is optional and the default value is 0.

sigmaX (optional) is a floating number indicating the standard deviation of X. It is optional and the default value is 1.

sigmaY (optional) is a floating number indicating the standard deviation of Y. It is optional and the default value is 1.

confLevel (optional) is a floating number between 0 and 1 indicating the confidence level of the test. It is optional and the default value is 0.95.

If Y is not specified, conduct a one-sample Z-test on X. If Y is specified, conduct a paired-sample Z-test on X and Y.

Return a dictionary with the following keys:

• stat: a table with p-value and confidence interval under 3 alternative hypotheses.

• confLevel: confidence level

• method: "One sample Z-test" if Y is not specified; "Two sample Z-test" if Y is specified.

• zValue: Z-stat

One-sample Z-test:

x = norm(5.0, 2.0, 30)
zTest(x, , 5.0, 2.0);

// output
stat->

alternativeHypothesis       pValue   lowerBound upperBound
--------------------------- -------- ---------- -----------
true mean is not equal to 5 0.035765 3.517659   4.949014
true mean is less than 5    0.017882 -Infinity  4.833952
true mean is greater than 5 0.982118 3.632721   Infinity

confLevel->0.95
method->One sample z-test
zValue->-2.099594

Paired-sample Z-test:

x = norm(5.0, 2.0, 30)
y = norm(10.0, 3.0, 40)
zTest(x, y, -5.0, 2.0, 3.0);

// output
stat->

------------------------------------- -------- ---------- -----------
alternativeHypothesis                 pValue   lowerBound upperBound
difference of mean is not equal to -5 0.976133 -6.191162  -3.844655
difference of mean is less than -5    0.488067 -Infinity  -4.033283
difference of mean is greater than -5 0.511933 -6.002533  Infinity

confLevel->0.95
method->Two sample z-test
zValue->-0.029917