[R] relationship between t-test CI and SEM?

[Rob Campbell]

Hi,

I have what is probably a stupid question but I'm confused so here goes:

- I have a distribution (n=100) and want to determine if the mean is 
significantly different from 0.5.
- When I plot the 2-tailed 95% confidence limits for the standard error 
of the mean I find that the upper one just overlaps with 0.5. I was 
under the impression that this would lead me to conclude that there was 
no significant difference between the sample mean and 0.5.
- However, when I perform a t-test it tells me that my mean /is/ 
significantly different from 0.5. The confidence intervals returned by 
the t-test don't seem to match with the SEM I calculated (lm does return 
the same intervals).

I have tried this in both R and matlab with the same results. So I think 
I'm calculating things right. Am I misinformed about the interpretation 
of the SEM? What are the confidence limits returned by the t-test (they 
bear no relationship to the SEM)?


Thanks!

Rob