[R] Question about interpretation of paired t-tests

[Beat Meier]

hi there,

i have a few questions about the correct interpretation of a paired t-test.
(i don't think that this matters, but I'm using R 2.10.1 on Windows).

to my questions:

i've been using a lot of time about this minor concerns now and I hope 
you can help me...

I use one- and two-sided t-tests. My questons are on one side about how 
R uses the hypothesis' and the second one is about p-vaues. First the 
one-sided:

 > t.test(var1,var2,paired=T,alternative="g")

         Paired t-test

data:  var1 and var2
t = 4.3456, df = 50, p-value = 3.401e-05
alternative hypothesis: true difference in means is greater than 0
95 percent confidence interval:
  0.00825842        Inf
sample estimates:
mean of the differences
              0.01344257

This tests (H0-Hypothesis), whether the difference in means is smaller 
or equal to 0? Here, the p-value is smaller than 0.05, which should mean 
that at a level of 95% one can't reject the H0-hypothesis? there is no 
strong evidence for rejecting the hypothesis, that the difference in 
means is smaller or equal to 0?
(Question is, if I write "alternative="g"", if this defines my 
alternative hypothesis (difference in means > 0) which I couldn't reject 
if the p-value was >0.05?)

The two-sided:
 > t.test(var1,var2,paired=T,alternative="t")

         Paired t-test

data:  var1 and var2
t = 4.3456, df = 50, p-value = 6.801e-05
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
  0.007229405 0.019655737
sample estimates:
mean of the differences
              0.01344257

This tests, whether the difference in means is 0. p-value is smaller 
than 0.025 (alpha/2) at a level of 95%, so the hypothesis that the 
difference in means is 0 can't be rejected?


Thanks a lot,
B. Meier