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 9 degrees of freedom. nothing ​(Round to three decimal places as​ needed.)

​(b) Find the​ t-value such that the area in the right tail is 0.05 with 16 degrees of freedom. nothing ​(Round to three decimal places as​ needed.)

​(c) Find the​ t-value such that the area left of the​ t-value is 0.15 with 5 degrees of freedom.​ [Hint: Use​ symmetry.] nothing ​(Round to three decimal places as​ needed.)

​(d) Find the critical​ t-value that corresponds to 95 ​% confidence. Assume 9 degrees of freedom.

Answer 1

Solution :

Given that,

a) Area = = 0.25

Right tail test

Degrees of freedom = df =9

t _,df = t_0.25,9 = 0.703

t value = 0.703

b)

Area = = 0.05

Right tail test

Degrees of freedom = df = 16

t _,df = t_0.05,16 = 1.746

t value = 1.746

c)

Area = = 0.15

Left tail test

Degrees of freedom = df = 5

t _,df = t_0.15= -1.156

t value = -1.156

d) Degrees of freedom = df = 9

At 95% confidence level

= 1-0.95% =1-0.95 =0.05

/2 =0.05/ 2= 0.025

t_/2,df = t_{0.025,9 = 2.262}

Critical t value = 2.262