Usage

`javascript
var ztest = require( '@stdlib/stats-ztest' );
`

#### ztest( x, sigma\[, opts] )

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

`javascript
var normal = require( '@stdlib/random-array-normal' );

// Create an array of random numbers:
var arr = normal( 300, 0.0, 2.0 );

// Test whether true mean is equal to 0.0:
var out = ztest( arr, 2.0 );
/* e.g., returns
{
'rejected': false,
'pValue': ~0.155,
'statistic': ~-1.422,
'ci': [~-0.391,~0.062],
// ...
}
*/
`

The returned object comes with a .print() method which when invoked will print a formatted output of the hypothesis test results. print accepts a digits option that controls the number of decimal digits displayed for the outputs and a decision option which when set to false will hide the test decision.

`javascript
var table = out.print({
'digits': 3
});
console.log( table );
/* e.g., =>
One-sample z-test

Alternative hypothesis: True mean is not equal to 0

pValue: 0.155
statistic: -1.422
95% confidence interval: [-0.391,0.062]

Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/
`

The ztest function accepts the following options:

- alpha: number in the interval [0,1] giving the significance level of the hypothesis test. Default: 0.05.
- alternative: Either two-sided, less or greater. 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.
- mu: number denoting the hypothesized true mean under the null hypothesis. Default: 0.

By default, the hypothesis test is carried out at a significance level of 0.05. To choose a different significance level, set the alpha option.

`javascript
var arr = [ 2, 4, 3, 1, 0 ];

var out = ztest( arr, 2.0, {
'alpha': 0.01
});

var table = out.print();
/* e.g., returns
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
*/

out = ztest( arr, 2.0, {
'alpha': 0.1
});
table = out.print();
/* e.g., returns
One-sample z-test

Alternative hypothesis: True mean is not equal to 0

pValue: 0.0253
statistic: 2.2361
90% confidence interval: [0.5288,3.4712]

Test Decision: Reject null in favor of alternative at 10% significance level
*/
`

To test whether the data comes from a distribution with a mean different than zero, set the mu option.

`javascript
var arr = [ 4, 4, 6, 6, 5 ];

var out = ztest( arr, 1.0, {
'mu': 5.0
});
/* e.g., returns
{
'rejected': false,
'pValue': 1.0,
'statistic': 0.0,
'ci': [ ~4.123, ~5.877 ],
// ...
}
*/
`

By default, a two-sided test is performed. To perform either of the one-sided tests, set the alternative option to less or greater.

`javascript
var arr = [ 4, 4, 6, 6, 5 ];

var out = ztest( arr, 1.0, {
'alternative': 'less'
});

var table = out.print();
/* e.g., returns
One-sample z-test

Alternative hypothesis: True mean is less than 0

pValue: 1.0
statistic: 11.1803
95% confidence interval: [-Infinity,5.7356]

Test Decision: Fail to reject null in favor of alternative at 5% significance level
*/

out = ztest( arr, 1.0, {
'alternative': 'greater'
});
table = out.print();
/* e.g., returns
One-sample z-test

Alternative hypothesis: True mean is greater than 0

pValue: 0.0
statistic: 11.1803
95% confidence interval: [4.2644,Infinity]

Test Decision: Reject null in favor of alternative at 5% significance level
*/
`