Question

Find the critical value t* for the following situations.

​a) a 95​% confidence interval based on df=19

​b) a 90​%confidence interval based on df=9

Answer 1

Solution :

Given that,

a)

Degrees of freedom = df = 19

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,19 = 2.093

The critical value t* 2.093

b)

Degrees of freedom = df = 9

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t /2,df = t0.05,9 = 1.833

The critical value t* 1.833