Complete parts (a) through (c) below.
(a) determine the critical value(s) for a right-tailed test of a population mean at the alphaequals0.01 level of significance with 10 degrees of freedom.
(b) determine the critical value(s) for a left-tailed test of a population mean at the alphaequals0.10 level of significance based on a sample size of nequals15.
(c) determine the critical value(s) for a two-tailed test of a population mean at the alphaequals0.01 level of significance based on a sample size of nequals12.

a) t =  2.7638

b) t = - 2.6245

c) t = 3.1058      on the right side    and

   t  = -3.1058    on the left

Step-by-step explanation:

a)Determine critical value for a right-tail test  for α = 0.01 level of significance and 10 degrees of fredom

From t-student table we find:

gl  =  10   and α = 0.01       ⇒  t =  2.7638

b)Determine   critical value for a left-tail test  for α = 0.01 level of significance  and sample size n = 15

From t-student table we find:

gl  =  14   and α = 0.01           gl  =  n - 1      gl  = 15 - 1    gl = 14

t = - 2.6245

c) Determine critical value for a two tails-test  for α = 0.01 level of  significance the  α/2   =   0.005  and sample size  n = 12

Then

gl  =  11   and α = 0.005

t = 3.1058      on the right side of the curve and by symmetry

t = - 3.1058  

From t-student table we find: