Determine the critical value(s) of the test statistic for each of the following small sample tests for the population mean where the assumption of normality is satisfied. round your answer to four decimal places.

step 1 of 3:

left-tailed test,α=0.01,n=19

step 2 of 3:

right-tailed test ,α=0.1,n=13

step 3 of 3:

two-tailed test, α=0.05,n=17

Step 1  t  = - 2.552

Step 2 t   =  1.356

Step 3  two values     t  =  - 2.12 on the left   and   t = 2.12 on the right

Step-by-step explanation:

Normal Distribution

size sample  < 30

Table to use  t-student table

a)  left-tailed test       α  =  0,01            n = 19      gl   = 19 -1      gl = 18

Directly from  t table      

t  = - 2.552

b) Right-tailed test     α  = 0,1     n  = 13     gl  = 13 - 1    gl =12

Directly from  t table

t  = 1.356

c)  Two-tailed test   α  = 0,05   but two tails means   we use α/2

    α/2  =  0,025    n = 17   gl  = n - 1   gl  = 17  -1     gl  = 16

From table:

t =  - 2.12  on the left tail  and  t = 2.12 on the right tail

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so:

the answer is simply just 6n add the two together as they have an n