# MeanCIn: Sample Size for a Given Width of a Confidence Interval for a Mean

## Description

Returns the required sample size to obtain a given width of a confidence interval for the sample mean. The function uses `uniroot()`

to find a numeric solution. The t distribution is used.

## Usage

MeanCIn(ci, sd, interval = c(2, 100000), conf.level = 0.95,
norm = FALSE, tol = .Machine$double.eps^0.5)

## Arguments

- ci
the left and right bound of the interval, which is presumed to be symmetric.

- sd
the standard deviation of the sample.

- interval
the interval for the sample size to be searched into, (default is c(2, 100000)).

- conf.level
confidence level, defaults to `0.95`

.

- norm
logical, determining if the t- or normaldistribution should be used.

- tol
the desired accuracy (convergence tolerance).

## Author

Andri Signorell <andri@signorell.net>

## Details

The required sample sizes for a specific width of confidence interval for the mean depends recursively on the sample size, as the samplesize defines the degrees of freedom in the t-distribution. Although in most practical cases it will be sufficient to use the normal distribution, we might be interested in exact results.