Question

The variable x has a t distribution with 18 degrees of freedom. What is the probability that an observed x is greater than 1?

Answer 1

Solution:

Given: The variable x has a t distribution with 18 degrees of freedom.

We have to find:

P( X > 1) = ..........?

To get exact probability , we need to use Excel command or TI 84 plus calculator.

Excel command:

=T.DIST.RT( x , df )

where x = t value = 1 and df = degrees of freedom = 18

Thus we get:

=T.DIST.RT( 1 , 18 )

=0.165282

=0.1653

That is: P( X > 1 ) = 0.1653

TI-84 plus calculator:

Use following steps:

Step 1) Press 2ND and VARS

Step 2) Select tcdf(

Step 4) Enter numbers:

Note Upper limit should be infinity , so I entered very large number 9999999.

Click on Paste and press ENTER two times.

Thus we get:

P( X > 1 ) = 0.1652824657

P( X > 1) = 0.1653