# T- distribution confusion

1. Nov 24, 2017

### tzx9633

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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2. Nov 24, 2017

### Ray Vickson

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
3. Nov 24, 2017

### WWGD

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?

4. Nov 25, 2017

### tzx9633

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 ?

5. Nov 25, 2017

### tzx9633

the question is find
P (T < ?? ) , v= 26 , α = 0.005

6. Nov 26, 2017

### Ray Vickson

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.

7. Nov 26, 2017

### tzx9633

Back to the question , should the ans be P (T < -2.779)???

8. Nov 26, 2017

### Ray Vickson

9. Nov 26, 2017

### WWGD

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 $P(t<T) < 0.05$ ?

10. Nov 26, 2017

### tzx9633

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) ??

11. Nov 26, 2017

### WWGD

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?

12. Nov 26, 2017

### tzx9633

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 $P(T<-2.279)$ ?

13. Nov 26, 2017

### Ray Vickson

Are you saying that if you know $P(T > w) = p$ you cannot figure out how to find $P(T < w)?$

14. Nov 27, 2017

### tzx9633

yes , i am only familiar with normal distribution , but not sure about t -distribution , can i do so for the t-distribution ?

15. Nov 27, 2017

### Ray Vickson

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.