Results 1 to 7 of 7

Math Help - confidence limits

  1. #1
    Member
    Joined
    Apr 2006
    Posts
    201
    Awards
    1

    Post confidence limits

    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
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by dadon View Post
    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:

    Code:
    >
    >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 
    >
    >
    RonL
    Last edited by CaptainBlack; January 13th 2007 at 08:51 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Apr 2006
    Posts
    201
    Awards
    1
    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
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by dadon View Post
    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?)
    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.

    also this line:

    [m-2.26*s,m+2.26*s]

    i cnt seem to get the same answers..
    There is a typo, for a 95% region for the mean that should have been

    [m-2.26*s/sqrt(N),m+2.26*s/sqrt(N)]


    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
    The sample size was 10, the degrees of freedom is N-1, see the article the
    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
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Apr 2006
    Posts
    201
    Awards
    1

    Post

    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
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by dadon View Post
    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
    m-(2.26*s/sqrt(N))=-0.692714-(2.26*1.19313)/sqrt(10)=-1.54541.

    so what did you do for the lower limit?

    RonL
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Apr 2006
    Posts
    201
    Awards
    1

    Thumbs up

    do the same for positive.


    thanks cheer captain

    i was doing the sum in ms excel and left the brackets outs.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Confidence Limits
    Posted in the Statistics Forum
    Replies: 0
    Last Post: March 2nd 2012, 02:58 PM
  2. Confidence limits
    Posted in the Statistics Forum
    Replies: 3
    Last Post: March 23rd 2011, 06:41 PM
  3. Confidence limits for non normal distribution
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: October 29th 2009, 04:57 PM
  4. confidence level and confidence interval?
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: July 12th 2009, 07:59 AM
  5. Minitab help - confidence limits
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: May 11th 2009, 08:27 PM

Search Tags


/mathhelpforum @mathhelpforum