z.test {BSDA} | R Documentation |

## Z-test

### Description

This function is based on the standard normal distribution and creates confidence intervals and tests hypotheses for both one and two sample problems.

### Usage

```
z.test(
x,
y = NULL,
alternative = "two.sided",
mu = 0,
sigma.x = NULL,
sigma.y = NULL,
conf.level = 0.95
)
```

### Arguments

`x` |
numeric vector; |

`y` |
numeric vector; |

`alternative` |
character string, one of |

`mu` |
a single number representing the value of the mean or difference in means specified by the null hypothesis |

`sigma.x` |
a single number representing the population standard
deviation for |

`sigma.y` |
a single number representing the population standard
deviation for |

`conf.level` |
confidence level for the returned confidence interval, restricted to lie between zero and one |

### Details

If `y`

is `NULL`

, a one-sample z-test is carried out with
`x`

. If y is not `NULL`

, a standard two-sample z-test is
performed.

### Value

A list of class `htest`

, containing the following components:

`statistic` |
the z-statistic, with names attribute |

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

`conf.int` |
is a confidence
interval (vector of length 2) for the true mean or difference in means. The
confidence level is recorded in the attribute |

`estimate` |
vector of
length 1 or 2, giving the sample mean(s) or mean of differences; these
estimate the corresponding population parameters. Component |

`null.value` |
is the
value of the mean or difference in means specified by the null hypothesis.
This equals the input argument |

`alternative` |
records the
value of the input argument alternative: |

`data.name` |
a character string (vector of length
1) containing the actual names of the input vectors |

### Null Hypothesis

For the one-sample z-test, the null hypothesis is
that the mean of the population from which `x`

is drawn is `mu`

.
For the standard two-sample z-tests, the null hypothesis is that the
population mean for `x`

less that for `y`

is `mu`

.

The alternative hypothesis in each case indicates the direction of
divergence of the population mean for `x`

(or difference of means for
`x`

and `y`

) from `mu`

(i.e., `"greater"`

,
`"less"`

, `"two.sided"`

).

### Author(s)

Alan T. Arnholt

### References

Kitchens, L.J. (2003). *Basic Statistics and Data
Analysis*. Duxbury.

Hogg, R. V. and Craig, A. T. (1970). *Introduction to Mathematical
Statistics, 3rd ed*. Toronto, Canada: Macmillan.

Mood, A. M., Graybill, F. A. and Boes, D. C. (1974). *Introduction to
the Theory of Statistics, 3rd ed*. New York: McGraw-Hill.

Snedecor, G. W. and Cochran, W. G. (1980). *Statistical Methods, 7th
ed*. Ames, Iowa: Iowa State University Press.

### See Also

### Examples

```
x <- rnorm(12)
z.test(x,sigma.x=1)
# Two-sided one-sample z-test where the assumed value for
# sigma.x is one. The null hypothesis is that the population
# mean for 'x' is zero. The alternative hypothesis states
# that it is either greater or less than zero. A confidence
# interval for the population mean will be computed.
x <- c(7.8, 6.6, 6.5, 7.4, 7.3, 7., 6.4, 7.1, 6.7, 7.6, 6.8)
y <- c(4.5, 5.4, 6.1, 6.1, 5.4, 5., 4.1, 5.5)
z.test(x, sigma.x=0.5, y, sigma.y=0.5, mu=2)
# Two-sided standard two-sample z-test where both sigma.x
# and sigma.y are both assumed to equal 0.5. The null hypothesis
# is that the population mean for 'x' less that for 'y' is 2.
# The alternative hypothesis is that this difference is not 2.
# A confidence interval for the true difference will be computed.
z.test(x, sigma.x=0.5, y, sigma.y=0.5, conf.level=0.90)
# Two-sided standard two-sample z-test where both sigma.x and
# sigma.y are both assumed to equal 0.5. The null hypothesis
# is that the population mean for 'x' less that for 'y' is zero.
# The alternative hypothesis is that this difference is not
# zero. A 90% confidence interval for the true difference will
# be computed.
rm(x, y)
```

*BSDA*version 1.2.2 Index]