hey!
I was wondering if anyone knew anything about 95% confidence limits from a 't' distribution?
..and if it is possible an example.
thanks.
dadon
The Wikipedia article on the t-distribution is very good and can be found here
A example is shown in the following code block showing a computer session
computing a 95% confidence interval for the mean:
RonLCode:> >N=10; >x=normal(N,1) -0.309911 -2.01066 -0.568246 -1.0841 -0.277172 -1.4568 0.658046 1.53204 -2.47296 -0.937381 >m=mean(x') -0.692714 > >s=sqrt(sum((x'-m)^2)/(N-1)) 1.19313 > >..95% region for T-distribution with 9 DF is +/-2.26 (looked up >..in a table of the T-distribution) > >..so the 95% region for the sample mean is m+/-2.26*s/sqrt(N) > >[m-2.26*s/sqrt(N),m+2.26*s/sqrt(10)] -1.54541 0.159986 > >
thanks for that captain.
im abit confused:
s=sqrt(sum((x'-m)^2)/(N-1))
(could you please put in the values for x', m, and N and wot is s?)
also this line:
[m-2.26*s,m+2.26*s]
i cnt seem to get the same answers..
is this a general way of finding the confidence limits?
and also wots the difference in the the amount of degree of freedom you use and why is it 9 DF for this case.
thanks
s is the sample stadard deviation, x is a array containing the sample
(from a standard normal population), m is the sample mean calculated
on the previous line by mean(x'), and N is the sample size set at the top
to 10.
The ' on the x's are transposition operators because the sum and mean
functions require row data vectors withe x is a column vector.
There is a typo, for a 95% region for the mean that should have beenalso this line:
[m-2.26*s,m+2.26*s]
i cnt seem to get the same answers..
[m-2.26*s/sqrt(N),m+2.26*s/sqrt(N)]
The sample size was 10, the degrees of freedom is N-1, see the article theis this a general way of finding the confidence limits?
and also wots the difference in the the amount of degree of freedom you use and why is it 9 DF for this case.
thanks
I gave you a link for for futher explanation.
The DF are needed as we are doing small sample statistics, and the sample
size affects the distributions involved.
RonL
hey thanks captain!
i checked the link you gave. quite good!
according to thier table 95% is 1.83 but you probably read the next coulmn for 97.5% which is 2.26 (for 9DF)
(still using 2.26) but i still can't get the answer for this line:
[m-2.26*s/sqrt(N),m+2.26*s/sqrt(10)]
-1.54541, 0.159986
i get:
-1.11406 and 0.59134
am I doing something wrong?
thanks
dadon