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

[Zembower, Kevin]

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
111 Market Place, Suite 310
Baltimore, Maryland  21202
410-659-6139