For df=25, determine the value of A that corresponds to each of the following probabilities:
a) P(t ≥A) =0.025
b) P(t ≤ A) =0.10
c) P (-A ≤ t ≤ A) =0.99
I am not sure that I am understanding your question, as the problem I entered is as it is listed in my book, however my instructor explained it as this:
For df=25, determine the value of A that corresponds to each of the following probabilities:
a) P(t ≥A) =0.025
b) P(t ≤ A) =0.10
c) P (-A ≤ t ≤ A) =0.99
The
a) A = 2.060
b) P(t ≤ A) =0.10 implies P(t >= A) = 0.90
Thus, A = -1.316
c) Since t-distribution is symmetric, P (-A ≤ t ≤ A) =0.99 implies that we need to find A such that P(t >= A) = (1-0.99)/2=0.005
Thus, A = 2.787
How can I help you if you don't say what tools you've been given to answer questions like this. There are several ways of answering it.
Perhaps you're expected to use a table of critical values like the one found here: 1.3.6.7.2. Upper Critical Values of the Student's-t Distribution
In which case it is clear that the answers are:
a) 2.060
b) and c) Your instructor has already outlined how to do it. The numbers your instructor used are got from tables like in the one in the above hyperlink.
If you cooperated by answering the questions I asked it would have been easier to help you.
By the way, the reason I asked what distribution A followed is that many distributions are characterised by degree of freedom. Without knowing which one in particular it was impossible to help you without having to make a guess which one .... Why guess, I thought, when I can simply ask for clarification ....... The fact that you could not tell me suggests you have deeper problems than the one you posted - you're advised to get as much help as possible from your instructor.
Furthermore, even when the distribution is known, their are several ways of answering the question. Numerical integration of the pdf, black-box technology, tables of critical values etc. Again, why guess, I thought, when I can simply ask for clarification .......