{{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 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 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 --------