Answers:
P(t ≤ 2.00) = 0.97153
c = 2.818756
Solution:
Consider a t distribution with 24 degrees of freedom. Compute P(t≤2.00)
We are given
df = 24
P(t ≤ 2.00) = 1 - P(t > 2.00)
P(t > 2.00) = 0.02847
(by using calculator/excel)
P(t ≤ 2.00) = 1 - 0.02847
P(t ≤ 2.00) = 0.97153
Now, we are given
df = 22
P(-c < t < c) = 0.99
This implies that
P(t < -c) + P(t > c) = 1 - 0.99 = 0.01
For t distribution, we have
P(t < -c) = P(t > c)
So, we have
2* P(t > c) = 0.01
P(t > c) = 0.005
So, the required value of c by using calculator or excel is given as below:
c = 2.818756
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