Question

Determine the critical​ t-scores for each of the conditions below.

​a)	​one-tail test, alphaαequals=0.01, and nequals=38
​b)	​one-tail test, alphaαequals=0.005, and nequals=10
​c)	​two-tail test, alphaαequals=0.05 and nequals=25
​d)	​two-tail test, alphaα=0.10 and n=13

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​a) The critical​ t-score(s) for a​ one-tail test, where

alphaα=0.01​,

and

n=38

​is(are)

nothing.

​(Round to three decimal places as needed. Use a comma to separate answers as​ needed.)

​b) The critical​ t-score(s) for a​ one-tail test, where

alphaα=0.005

and

n=10

​is(are)

nothing.

​(Round to three decimal places as needed. Use a comma to separate answers as​ needed.)

​c) The critical​ t-score(s) for a​ two-tail test, where

alphaα=0.05​,

and

n=2

​is(are)

nothing.

​(Round to three decimal places as needed. Use a comma to separate answers as​ needed.)

​d) The critical​ t-score(s) for a​ two-tail test, where

alphaαequals=0.10

and

n=13

​is(are)

nothing.

​(Round to three decimal places as needed. Use a comma to separate answ

Answer 1

Solution :

Given that,

(a)

sample size = n = 38

Degrees of freedom = df = n - 1 = 38 - 1 = 37

= 0.01

t _,df = t _0.01,37 = 2.431

critical t score = 2.431

(b)

sample size = n = 10

Degrees of freedom = df = n - 1 = 10 - 1 = 9

= 0.005

t _,df = t _0.005,9 = 3.250

critical t score = 3.250

(c)

sample size = n = 2

Degrees of freedom = df = n - 1 = 2 - 1 = 1

= 0.05

/ 2 = 0.05 / 2 = 0.025

t_{/2 ,df} = t _0.025,1 = -/+12.706

critical t score = -12.706 , +12.706

(d)

sample size = n = 13

Degrees of freedom = df = n - 1 = 13 - 1 = 12

= 0.10

/ 2 = 0.10 / 2 = 0.05

t_{/2 ,df} = t _0.05,12 = -/+1.782

critical t score = -1.782 , +1.782