repl.txt

{{alias}}( x, sigma[, options] )
    Computes a one-sample z-test.

    The function performs a one-sample z-test for the null hypothesis that the
    data in array or typed array `x` is drawn from a normal distribution with
    mean zero and standard deviation `sigma`.

    The returned object comes with a `.print()` method which when invoked will
    print a formatted output of the results of the hypothesis test.

    Parameters
    ----------
    x: Array<number>
        Data array.

    sigma: number
        Known standard deviation.

    options: Object (optional)
        Options.

    options.alpha: number (optional)
        Number in the interval `[0,1]` giving the significance level of the
        hypothesis test. Default: `0.05`.

    options.alternative: string (optional)
        Indicates whether the alternative hypothesis is that the mean of `x` is
        larger than `mu` (`greater`), smaller than `mu` (`less`) or equal to
        `mu` (`two-sided`). Default: `'two-sided'`.

    options.mu: number (optional)
        Hypothesized true mean under the null hypothesis. Set this option to
        test whether the data comes from a distribution with the specified `mu`.
        Default: `0`.

    Returns
    -------
    out: Object
        Test result object.

    out.alpha: number
        Used significance level.

    out.rejected: boolean
        Test decision.

    out.pValue: number
        p-value of the test.

    out.statistic: number
        Value of test statistic.

    out.ci: Array<number>
        1-alpha confidence interval for mean.

    out.nullValue: number
        Assumed mean value under H0.

    out.sd: number
        Standard error.

    out.alternative: string
        Alternative hypothesis (`two-sided`, `less` or `greater`).

    out.method: string
        Name of test (`One-Sample z-test`).

    out.print: Function
        Function to print formatted output.

    Examples
    --------
    // One-sample z-test:
    > var rnorm = {{alias:@stdlib/random/base/normal}}.factory( 0.0, 2.0, { 'seed': 212 } );
    > var x = new Array( 100 );
    > for ( var i = 0; i < x.length; i++ ) {
    ...     x[ i ] = rnorm();
    ... }
    > var out = {{alias}}( x, 2.0 )
    {
        alpha: 0.05,
        rejected: false,
        pValue: ~0.180,
        statistic: ~-1.34,
        ci: [ ~-0.66, ~0.124 ],
        ...
    }

    // Choose custom significance level and print output:
    > arr = [ 2, 4, 3, 1, 0 ];
    > out = {{alias}}( arr, 2.0, { 'alpha': 0.01 } );
    > table = out.print()
    One-sample z-test

    Alternative hypothesis: True mean is not equal to 0

        pValue: 0.0253
        statistic: 2.2361
        99% confidence interval: [-0.3039,4.3039]

    Test Decision: Fail to reject null in favor of alternative at 1%
    significance level


    // Test for a mean equal to five:
    > var arr = [ 4, 4, 6, 6, 5 ];
    > out = {{alias}}( arr, 1.0, { 'mu': 5 } )
    {
        rejected: false,
        pValue: 1,
        statistic: 0,
        ci: [ ~4.123, ~5.877 ],
        // ...
    }

    // Perform one-sided tests:
    > arr = [ 4, 4, 6, 6, 5 ];
    > out = {{alias}}( arr, 1.0, { 'alternative': 'less' } )
    {
        alpha: 0.05,
        rejected: false,
        pValue: 1,
        statistic: 11.180339887498949,
        ci: [ -Infinity, 5.735600904580115 ],
        // ...
    }
    > out = {{alias}}( arr, 1.0, { 'alternative': 'greater' } )
    {
        alpha: 0.05,
        rejected: true,
        pValue: 0,
        statistic: 11.180339887498949,
        ci: [ 4.264399095419885, Infinity ],
        //...
    }

    See Also
    --------