Question

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.

Answer 1

a) t = 2.7638

b) t = - 2.6245

c) t = 3.1058 on the right side and

t = -3.1058 on the left

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: