Description Usage Arguments Details Value Null Hypothesis Author(s) References See Also Examples

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

1 2 |

`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 |

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.

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 |

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"`

).

Alan T. Arnholt

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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | ```
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)
``` |

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.