# [R] Homework help: Is this how CI using t dist are constructed?

Achim Zeileis Achim.Zeileis at wu-wien.ac.at
Tue Oct 30 21:52:53 CET 2007

```On Tue, 30 Oct 2007, Zembower, Kevin wrote:

> I'm trying to replicate some of the examples from my textbook in R (my
> text uses Minitab). In this problem, I'm trying to construct a 95%
> confidence interval for these distance measurements [1]:
>
> > # Case Study 7.4.1, p. 483
> > x <- scan()
> 1:  62 52 68 23 34 45 27 42 83 56 40
> 12:
> > alpha<-.95
> > mean(x) + qt(c((1-alpha)/2, 1-((1-alpha)/2)), df=length(x)-1) * sd(x)
> / sqrt(length(x))
> [1] 36.21420 60.51307
> >
>
> Are confidence intervals with the t distribution constructed using this
> type of equation, or am I overlooking a more concise, 'canned' approach
> that's already been programmed? Any suggestions on simplifying this?

R offers a confint() generic with methods for various types of models.
If you consider estimation of the mean as a simple linear model (with only
an intercept) you can do
fm <- lm(x ~ 1)
fm
to estimate the mean and then
confint(fm)
to get the confidence interval (by default at 0.95 level).

hth,
Z

>
> -Kevin
>
> [1] An Introduction to Mathematical Statistics and its Applications,
> fourth ed., Larsen and Marx.
>
> Kevin Zembower
> Internet Services Group manager
> Center for Communication Programs
> Bloomberg School of Public Health
> Johns Hopkins University
> 111 Market Place, Suite 310
> Baltimore, Maryland  21202
> 410-659-6139
>
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