Question

Find the critical value t* for the following situations.

​a) a 98​% confidence interval based on df=21

​b) a 95​% confidence interval based on df=5

Answer 1

Solution :

Given that,

a)

Degrees of freedom = df = 21

At 98% confidence level the t is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

t /2,df = t0.01,21 = 2.518

Critical value t* 2.518

b)

Degrees of freedom = df = 5

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,5 = 2.571

Critical value t* 2.571