ported/confidence_test_family

pub fn z_test_kernel(
    values: &[f64],
    x: f64,
    sigma: Option<f64>,
) -> Result<f64, WorksheetErrorCode> {
    if values.is_empty() || !x.is_finite() {
        return Err(WorksheetErrorCode::Value);
    }
    let mean = values.iter().sum::<f64>() / values.len() as f64;
    let sigma = match sigma {
        Some(value) => value,
        None => stdev_from_values(values, VarianceDivisor::Sample)?,
    };
    if sigma <= 0.0 || !sigma.is_finite() {
        return Err(WorksheetErrorCode::Num);
    }
    // Live Excel 16.0 b20326: Z.TEST(array,x) with omitted sigma is
    // NORMSDIST((x-AVERAGE)/(STDEV.S/SQRT(n))), not 1-NORMSDIST((mean-x)/se)
    // and not STDEV.P. The two NORMSDIST complements are not bit-identical.
    // F1 (dc-8dq): (x - mean) * sqrt(n) / sigma, as Excel's Z.TEST gives Z.TEST({1,5,3},2) (the
    // catalogue oracle's capture); dividing by sigma/sqrt(n) is one ulp away there.
    let z = (x - mean) * (values.len() as f64).sqrt() / sigma;
    crate::ported::normal_log_family::norm_s_dist_kernel(z, true)
}