Question

Let 'c' represent the area under a t-distribution curve with eight degrees of freedom that lies between two values -tx and tx. Find the value of LaTeX: t_x t x that is associated to the following values of 'c'. (Round to 2 decimal places)

a) c = 0.95, tx=

b) c = 0.97, t x =

c) c = 0.99, t x =

d) c = 0.995, t x =

Answer 1

Solution :

Given that,

sample size = n = 8

Degrees of freedom = df = n - 1 = 8 - 1 = 7

a) At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

t/2,df = 2.365

b) At 97% confidence level

= 1 - 97%  

= 1 - 0.97 = 0.03

/2 = 0.015

t/2,df = 2.715

c) At 99% confidence level

= 1 - 99%

=1 - 0.99 =0.01

/2 = 0.005

t/2,df = 3.499

d) At 99.5% confidence level

= 1 - 99.5%

=1 - 0.995 = 0.005

/2 = 0.0025

t/2,df = 4.029