[R] How would you calculate this type of p-value using R?

[RQuestion]

Let's say you want to compare "one observation" with a sample, how would you
use R to get a p-value for that single observation itself?


To clarify what I'm asking: We know you use a one-sample t test to compare
an actual sample to a hypothetical value, and a Wilcoxon test if it's not
normally distributed, in R either "t.test( )" or "wilcox.test( )". However,
what do you use if you don't want a p-value for a sample itself, but instead
want to get a *p-value for the likelihood that just "one observation" could
have its distance from a sample just by chance*?



Context for my question: Many of us know about the Casey Anthony case, and
how the medical examiner said they looked at the records and 100% of all
drownings were reported within one hour. It wasn't until a month after when
it was finally reported to the police the girl was missing by the
grandmother and even longer after that when Casey finally claimed it was
really a drowning rather than a "Zanny the Nanny" kidnapping the little
girl.

So, I want to write the medical examiner to see if I can get a list of how
long it took for each of the drownings to be reported (she mentioned in
court), then calculate a standard deviation and based on the sample size
come up with a p-value for when Cindy Anthony finally reported the grand
daughter missing 31 days later. Then another p-value for when Casey Anthony
finally claimed it was a drowning years later.

How would you calculate a p-value for something like this? I'm guessing the
sample will probably not be normally distributed, so what would I use from R
if that's case?  I'm still quite new to R, so if at all possible don't make
your answer too technical.

Thanks so much!

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