Question

For parts a and b , use technology to estimate the following.

a) The critical value of t for a 90 % confidence interval with df=2.

b) The critical value of t for a 95 % confidence interval with df=104.

Answer 1

Solution :

Given that,

a ) Degrees of freedom = df = 2

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

t _/2,df = t_0.05,2 = 2.920

The critical value of t = 2.902

b ) Degrees of freedom = df = 104

At 95% confidence level the t is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,104 = 1.983

The critical value of t = 1.983