Question

Let to be a specific value of t. Use the table of critical values of t below to find to-values such that the following statements are true. a. P(- to <t<to) = 0.95, where df = 20 b. Patsto) = 0.01, where df = 13 c. Pts - to or t2to) = 0.10, where df=9 d. Pts - to ort2to) = 0.01, where df = 6 Click the icon to view the table of critical values of t. a. The value of to is (Type an integer or a decimal.) b. The value of tois (Type an integer or a decimal.) C. The value of to is (Type an integer or a decimal.) d. The value of to is (Type an integer or a decimal.)

Answer 1

a) We are to find to here such that:
P( -t0 < t < t0) = 0.95

Therefore, due to symmetry, we have here:
P( t < t0 ) = 0.95 + (1 - 0.95)/2 = 0.975

For 20 degrees of freedom, we have from the t distribution tables:
P( t20 < 2.086 ) = 0.975

Therefore 2.086 is the required value here.

b) For 13 degrees of freedmom, we have from the t distribution tables:
P( t13 < -2.650) = 0.01

Therefore -2.650 is the required t value here.

c) We have here:
P( t <= -t0 or t >= t0) = 0.1

Therefore, P( -t0 < t < t0) = 1 - 0.1 = 0.9

Therefore, P( t < t0) = 0.95

For 9 degrees of freedom, we have from t distribution tables:
P( t9 < 1.833) = 0.95

Therefore 1.833 is the required t value here.

d) Similar to other part, we have here:

P( -t0 < t < t0) = 1 - 0.01 = 0.99

Therefore, P( t < t0) = 0.995

From t distribution tables for 6 degrees of freedom, we have here:
P( t < 3.707) = 0.995

Therefore 3.707 is the required t value here.