# CI.t.test: Student's t-Confidence Interval with Finite Population... In jmuOutlier: Permutation Tests for Nonparametric Statistics

## Description

Performs two-sided confidence interval on population mean, allowing for a finite population correction.

## Usage

 `1` ```CI.t.test(x, conf.level = 0.95, fpc = 1) ```

## Arguments

 `x` A nonempty numeric vector of data values. `conf.level` Confidence level of the interval, and should be between 0 and 1. `fpc` The finite population correction, and should be between 0 and 1.

## Details

The `fpc` is typically defined as 1-n/N, where `n` is the sample size, and `N` is the population size, for simple random sampling without replacement. When sampling with replacement, set `fpc=1` (default).

## Value

A confidence interval for the population mean.

## Note

The definition of `fpc` is based on the textbook by Scheaffer, Mendenhall, Ott, Gerow (2012), chapter 4.

## Author(s)

Steven T. Garren, James Madison University, Harrisonburg, Virginia, USA

## References

Scheaffer, R. L., Mendenhall, W., Ott, R. L., Gerow, K. G. (2012) Elementary Survey Sampling, 7th edition.

`t.test` and `plotCI`.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```# Sample 43 observations from a population of 200 numbers, and compute the 95% confidence interval. pop = sqrt(1:200) ; x1 = sample( pop, 43 ) ; print(sort(x1)) CI.t.test( x1, fpc = 1-length(x1)/length(pop) ) # Sample 14 observations from a Normal(mean=50, sd=5) distribution, # and compute the 90% confidence interval. x2 = rnorm( 14, 50, 5 ) ; print(sort(x2)) CI.t.test( x2, 0.9 ) ```

### Example output

``` [1]  1.414214  2.645751  4.690416  4.795832  5.567764  5.916080  6.164414
[8]  6.324555  6.480741  6.633250  7.348469  7.549834  7.681146  8.185353
[15]  8.246211  8.544004  9.055385  9.273618  9.486833  9.591663  9.797959
[22] 10.440307 10.630146 11.045361 11.180340 11.575837 11.789826 11.832160
[29] 12.206556 12.449900 12.529964 12.688578 12.727922 12.806248 13.076697
[36] 13.152946 13.228757 13.341664 13.379088 13.527749 13.820275 13.856406
[43] 14.000000
[1]  8.880504 10.686018
[1] 47.39202 48.18987 48.20609 48.20951 49.77378 50.84966 51.30538 53.99598
[9] 54.57457 56.14915 56.30249 58.80775 59.33009 60.61250
[1] 50.94740 55.29529
```

jmuOutlier documentation built on Aug. 6, 2019, 1:03 a.m.