Question

Complete parts ?(a) through ?(c) below. ?(a) Determine the critical? value(s) for a? right-tailed test of a population mean at the ? = 0.10 level of significance with 20 degrees of freedom. ?(b) Determine the critical? value(s) for a? left-tailed test of a population mean at the ? = 0.05 level of significance based on a sample size of n = 15. ?(c) Determine the critical? value(s) for a? two-tailed test of a population mean at the ? = 0.10 level of significance based on a sample size of n=14.

Answer 1

Solution :

Given that,

a ) = 0.10

Degrees of freedom = df = 20

/ 2 = 0.10 / 2 = 0.05

t _/2,df = t_0.05,20 = 1.725

The critical? value(s) for a? right-tailed = 1.725

b ) n = 15

Degrees of freedom = df = n - 1 = 15 - 1 = 14

= 0.05

   / 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,14 = 0.365

The critical? value(s) for a? left-tailed = 0.365

c ) n = 14

Degrees of freedom = df = n - 1 = 14 - 1 = 13

   = 0.10

   / 2 = 0.10/ 2 = 0.05

t _/2,df = t_0.05,13 = 2.160

The critical? value(s) for a? two-tailed = 2.160