ci.mu.z {asbio} R Documentation

## Z and t confidence intervals for mu.

### Description

These functions calculate t and z confidence intervals for μ. Z confidence intervals require specification (and thus knowledge) of σ. Both methods assume underlying normal distributions although this assumption becomes irrelevant for large sample sizes. Finite population corrections are provided if requested.

### Usage

```
ci.mu.z(data, conf = 0.95, sigma = 1, summarized = FALSE, xbar = NULL,
fpc = FALSE, N = NULL, n = NULL)

ci.mu.t(data, conf = 0.95, summarized = FALSE, xbar = NULL, sd = NULL,
fpc = FALSE, N = NULL, n = NULL)
```

### Arguments

 `data` A vector of quantitative data. Required if `summarized = FALSE` `conf` Confidence level; 1 - P(type I error). `sigma` The population standard deviation. `summarized` A logical statement specifying whether statistical summaries are to be used. If `summarized = FALSE`, then the sample mean and the sample standard deviation (`t.conf` only) are calculated from the vector provided in `data`. If `summarized = FALSE` then the sample mean `xbar`, the sample size `n`, and, in the case of `ci.mu.t`, the sample standard deviation `st.dev`, must be provided by the user. `xbar` The sample mean. Required if `summarized = TRUE`. `fpc` A logical statement specifying whether a finite population correction should be made. If `fpc = TRUE` then both the sample size `n` and the population size `N` must be specified. `N` The population size. Required if `fpc=TRUE` `sd` The sample standard deviation. Required if `summarized=TRUE`. `n` The sample size. Required if `summarized = TRUE`.

### Details

`ci.mu.z` and `ci.mu.t` calculate confidence intervals for either summarized data or a dataset provided in `data`. Finite population corrections are made if a user specifies `fpc=TRUE` and provides some value for `N`.

### Value

Returns a list of `class = "ci"`. Default printed results are the parameter estimate and confidence bounds. Other `invisible` objects include:

 `Margin` the confidence margin.

Ken Aho

### References

Lohr, S. L. (1999) Sampling: Design and Analysis. Duxbury Press. Pacific Grove, USA.

`pnorm`, `pt`

### Examples

```#With summarized=FALSE
x<-c(5,10,5,20,30,15,20,25,0,5,10,5,7,10,20,40,30,40,10,5,0,0,3,20,30)
ci.mu.z(x,conf=.95,sigma=4,summarized=FALSE)
ci.mu.t(x,conf=.95,summarized=FALSE)
#With summarized = TRUE
ci.mu.z(x,conf=.95,sigma=4,xbar=14.6,n=25,summarized=TRUE)
ci.mu.t(x,conf=.95,sd=4,xbar=14.6,n=25,summarized=TRUE)
#with finite population correction and summarized = TRUE
ci.mu.z(x,conf=.95,sigma=4,xbar=14.6,n=25,summarized=TRUE,fpc=TRUE,N=100)
ci.mu.t(x,conf=.95,sd=4,xbar=14.6,n=25,summarized=TRUE,fpc=TRUE,N=100)
```

[Package asbio version 1.7 Index]