zsum.test {BSDA} | R Documentation |

## Summarized 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 based on summarized information the user passes to the function.
Output is identical to that produced with `z.test`

.

### Usage

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

### Arguments

`mean.x` |
a single number representing the sample mean of |

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

`n.x` |
a single number representing the sample size for |

`mean.y` |
a single number representing the sample mean of |

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

`n.y` |
a single number representing the sample size for |

`alternative` |
is a character string, one of |

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

`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` |
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 names |

### 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 of
`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

```
zsum.test(mean.x=56/30,sigma.x=2, n.x=30, alternative="greater", mu=1.8)
# Example 9.7 part a. from PASWR.
x <- rnorm(12)
zsum.test(mean(x),sigma.x=1,n.x=12)
# 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.
# Note: returns same answer as:
z.test(x,sigma.x=1)
#
x <- c(7.8, 6.6, 6.5, 7.4, 7.3, 7.0, 6.4, 7.1, 6.7, 7.6, 6.8)
y <- c(4.5, 5.4, 6.1, 6.1, 5.4, 5.0, 4.1, 5.5)
zsum.test(mean(x), sigma.x=0.5, n.x=11 ,mean(y), sigma.y=0.5, n.y=8, 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.
# Note: returns same answer as:
z.test(x, sigma.x=0.5, y, sigma.y=0.5)
#
zsum.test(mean(x), sigma.x=0.5, n.x=11, mean(y), sigma.y=0.5, n.y=8,
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. Note: returns same answer as:
z.test(x, sigma.x=0.5, y, sigma.y=0.5, conf.level=0.90)
rm(x, y)
```

*BSDA*version 1.2.2 Index]