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Homework Help: T- distribution confusion

  1. Nov 24, 2017 #1
    1. The problem statement, all variables and given/known data

    I'm asked to find the P (T < ?? ) , v= 26 , α = 0.005
    2. Relevant equations



    3. The attempt at a solution
    From the table , we could notice that P (T > 2.779) , v= 26 , α = 0.005 ,
    So , i think the ans should be P (T < -2.779 ) , v= 26 , α = 0.005 ,

    But the ans is P (T < 2.779) , why ?
    Is the ans wrong ?
     

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  3. Nov 24, 2017 #2

    Ray Vickson

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    I depends on what the "##\alpha = 0.005##" is supposed to mean.

    If you are performing a right-tail test you would want an upper-tail probability of no more than 0.005, so you would be seeking ##t_R## giving ##P(T > t_R) = 0.005##, or ##P(T < t_R) = 0.995##. However, if you are performing a left-tail test you want a value of ##t_L## giving ##P(T < t_L) = 0.005##. So, you are being asked to find either ##t_R## or ##t_L##. Your included diagram and table assume a right-tail test.
     
    Last edited: Nov 24, 2017
  4. Nov 24, 2017 #3

    WWGD

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    Just look at the table in the intersection of the row for ##\alpha=0.005 ## and ##v=26##, it gives you precisely the value ##2.779##. What is the question?
     
  5. Nov 25, 2017 #4
    Yes , the table is for right tail test . I am provided with this table and i'm asked this question . So , the ans should be P (T < -2.779) , am i right ?
     
  6. Nov 25, 2017 #5
    the question is find
    P (T < ?? ) , v= 26 , α = 0.005
     
  7. Nov 26, 2017 #6

    Ray Vickson

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    That is badly stated: ##\alpha = 0.005## refers to the test, so that you want to find a critical value ##t_c## such that ##P(T > t_c) =0.005##. If you are being asked to solve
    $$ P(T < ?) = 0.005$$
    that is a completely different issue.
     
  8. Nov 26, 2017 #7
    Back to the question , should the ans be P (T < -2.779)???
     
  9. Nov 26, 2017 #8

    Ray Vickson

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    You tell me; it is your question, on your homework.
     
  10. Nov 26, 2017 #9

    WWGD

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    tzx : If I understand correctly, you are asking which numerical value , in a t-distribution with ##v=26## will give you a probability ##\alpha =0.05 ## or less. May I suggest a rephrase :
    Find a value T in a t-distribution with ##v=26##, so that ##P(t<T) < 0.05 ## ?
     
  11. Nov 26, 2017 #10
    ok , thanks , the question now is changed to : Find a value T in a t-distribution with ##v=26##, so that ##P(t<T) < 0.05 ## ?

    So , the ans is P (T < -2.779) ??
     
  12. Nov 26, 2017 #11

    WWGD

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    This is a sort of reverse of the standard problem of finding the probability ##P(T<t)##, where T is known. Instead, you find to find the value ##T ## so that the probability is less than ##\alpha =0.05## . Can you look at your table and take it from there?
     
  13. Nov 26, 2017 #12
    No , the table provided is for ##P(T>t)## , for ##P(T<t)## i am not sure , i just want to verify my concept , can i use ##P(T<-2.279)## ?
     
  14. Nov 26, 2017 #13

    Ray Vickson

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    Are you saying that if you know ##P(T > w) = p## you cannot figure out how to find ##P(T < w)?##
     
  15. Nov 27, 2017 #14
    yes , i am only familiar with normal distribution , but not sure about t -distribution , can i do so for the t-distribution ?
     
  16. Nov 27, 2017 #15

    Ray Vickson

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    You need to go back and review elementary probability. The question you are asking has nothing at all to do with whether you are dealing with the t-distribution, the normal distribution or any other continuous distribution at all.

    I am not going to answer the question, because that would be a violation of PF policy. But, I am serious: you need to review some very, very basic material.
     
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