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

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