The null hypothesis in kpss test (kpss.test())

is that 'x' is level or trend stationary. I did this
 

  > s<-rnorm(1000)
  > kpss.test(s)

 
        KPSS Test for Level Stationarity
 
  data:  s
  KPSS Level = 0.0429, Truncation lag parameter = 7,
p-value = 0.1
 
  Warning message:
  p-value greater than printed p-value in:
kpss.test(s)

My question is whether p=0.1 is a good number to
reject N0? 

On the other hand, I have a series r and did the 
following:

  > plot.ts(r)
  > kpss.test(r)

 
        KPSS Test for Level Stationarity
 
  data:  r
  KPSS Level = 3.1955, Truncation lag parameter = 7,
p-value = 0.01
 
  Warning message:
  p-value smaller than printed p-value in:
kpss.test(r)

So this says we can have more confidence in saying r
is _not_ stationary?

Should I worry about the warnings?

Thanks very much.
Weiguang

As help(kpss.test) tells you: kpss.test()
approximates the p values by
interpolation from a simulated table of critical
values. As p values
larger than 0.1 are typically regarded to be
non-significant and p
values smaller than 0.01 are typically regarded to
be highly
significant, the corresponding critical values are
only stored for the
range 0.1 to 0.01.

Hence...