[R] Homework help: t test hypothesis testing with summarized data?

Zembower, Kevin
Wed, 07 Nov 2007 19:53:03 -0000

Is this how a t hypothesis test is done when I don't have the actual
data, but just the summarized statistics:
> #Homework 9.2.6 [1]
> n<-31
> xbar<-3.10
> s_x<-1.469
> m<-57
> ybar<-2.43
> s_y<-1.35
> s_pooled<- (((n-1)*s_x^2) + ((m-1)*s_y^2)) / (n + m - 2)
> s_pooled
[1] 1.939521
> t_obs <- (xbar -  ybar) / (s_pooled * (sqrt(1/n + 1/m)))
> t_obs
[1] 1.547951
> qt(c(.025, .975), n+m-2)
[1] -1.987934  1.987934
> # Therefore, fail to reject H0 at the 0.05 level of significance
>

Or am I again overlooking a canned procedure or an easier calculation
using the t distribution.

Thank you for your continued advice and help.

-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
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Baltimore, Maryland  21202
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