Question

Determine the​ t-value in each of the cases.

​(a) Find the​ t-value such that the area in the right tail is 0.25 with 11 degrees of freedom. ​(Round to three decimal places as​ needed.) ​

(b) Find the​ t-value such that the area in the right tail is 0.01 with 23 degrees of freedom. ​(Round to three decimal places as​ needed.)

​(c) Find the​ t-value such that the area left of the​ t-value is 0.05 with 19 degrees of freedom.​ [Hint: Use​ symmetry.] ​(Round to three decimal places as​ needed.) ​

(d) Find the critical​ t-value that corresponds to 80​% confidence. Assume 7 degrees of freedom. ​(Round to three decimal places as​ needed.)

Answer 1

Solution,

a) degrees of freedom = 11

P( t > t ) = 0.25

= 1 - P( t < t ) = 0.25

= P( t < t ) = 1 - 0.25

= P( t < t ) = 0.75

= P( t < 0.697 ) = 0.75

t = 0.697

b) degrees of freedom = 23

P( t > t ) = 0.01

= 1 - P( t < t ) = 0.01

= P( t < t ) = 1 - 0.01

= P( t < t ) = 0.99

= P( t < 2.500 ) = 0.99

t = 2.500

c) degrees of freedom = 19

P( t < t ) = 0.05

= P( t < -1.729 ) = 0.05

t = -1.729

d) Degrees of freedom = df = 7

At 80% confidence level

= 1 - 80%

=1 - 0.80 =0.20

/2 = 0.10

t/2,df = t0.10,7 = 1.415