ZTest {DescTools} | R Documentation |

## Z Test for Known Population Standard Deviation

### Description

Compute the test of hypothesis and compute confidence interval on the mean of a population when the standard deviation of the population is known.

### Usage

```
ZTest(x, ...)
## Default S3 method:
ZTest(x, y = NULL, alternative = c("two.sided", "less", "greater"),
paired = FALSE, mu = 0, sd_pop, conf.level = 0.95, ... )
## S3 method for class 'formula'
ZTest(formula, data, subset, na.action, ...)
```

### Arguments

`x` |
numeric vector of data values. Non-finite (e.g. infinite or missing) values will be omitted. |

`y` |
an optional numeric vector of data values: as with x non-finite values will be omitted. |

`mu` |
a number specifying the hypothesized mean of the population. |

`sd_pop` |
a number specifying the known standard deviation of the population. |

`alternative` |
a character string specifying the alternative
hypothesis, must be one of |

`paired` |
a logical indicating whether you want a paired z-test. |

`conf.level` |
confidence level for the interval computation. |

`formula` |
a formula of the form |

`data` |
an optional matrix or data frame (or similar: see |

`subset` |
an optional vector specifying a subset of observations to be used. |

`na.action` |
a function which indicates what should happen when the data contain |

`...` |
further arguments to be passed to or from methods. |

### Details

Most introductory statistical texts introduce inference by using the z-test
and z-based confidence intervals based on knowing the population
standard deviation. However statistical packages often do not include
functions to do z-tests since the t-test is usually more appropriate
for real world situations. This function is meant to be used during
that short period of learning when the student is learning about
inference using z-procedures, but has not learned the t-based
procedures yet. Once the student has learned about the
t-distribution the `t.test()`

function should be used instead of this
one (but the syntax is very similar, so this function should be an
appropriate introductory step to learning `t.test()`

).

The formula interface is only applicable for the 2-sample tests.

### Value

A list with class "`htest`

" containing the following components:

`statistic` |
the value of the z-statistic. |

`p.value` |
the p-value for the test |

`conf.int` |
a confidence interval for the mean appropriate to the specified alternative hypothesis. |

`estimate` |
the estimated mean or difference in means depending on whether it was a one-sample test or a two-sample test. |

`null.value` |
the specified hypothesized value of the mean or mean difference depending on whether it was a one-sample test or a two-sample test. |

`alternative` |
a character string describing the alternative hypothesis. |

`method` |
a character string indicating what type of test was performed. |

`data.name` |
a character string giving the name(s) of the data. |

### Author(s)

Andri Signorell <andri@signorell.net>, based on R-Core code of `t.test`

,

documentation partly from Greg Snow <greg.snow@imail.org>

### References

Stahel, W. (2002) *Statistische Datenanalyse, 4th ed*, vieweg

### See Also

### Examples

```
x <- rnorm(25, 100, 5)
ZTest(x, mu=99, sd_pop=5)
# the classic interface
with(sleep, ZTest(extra[group == 1], extra[group == 2], sd_pop=2))
# the formula interface
ZTest(extra ~ group, data = sleep, sd_pop=2)
# Stahel (2002), pp. 186, 196
d.tyres <- data.frame(A=c(44.5,55,52.5,50.2,45.3,46.1,52.1,50.5,50.6,49.2),
B=c(44.9,54.8,55.6,55.2,55.6,47.7,53,49.1,52.3,50.7))
with(d.tyres, ZTest(A, B, sd_pop=3, paired=TRUE))
d.oxen <- data.frame(ext=c(2.7,2.7,1.1,3.0,1.9,3.0,3.8,3.8,0.3,1.9,1.9),
int=c(6.5,5.4,8.1,3.5,0.5,3.8,6.8,4.9,9.5,6.2,4.1))
with(d.oxen, ZTest(int, ext, sd_pop=1.8, paired=FALSE))
```

*DescTools*version 0.99.54 Index]