Question

• Consider a t distribution with

  19

  degrees of freedom. Compute

  P≤t−1.22

  . Round your answer to at least three decimal places.
• Consider a t distribution with

  10

  degrees of freedom. Find the value of

  c

  such that

  =P<−c<tc0.90

  . Round your answer to at least three decimal places.

Answer 1

Solution:

Question 1)

Given: a t distribution with 19 degrees of freedom.

Compute:

P( t ≤ −1.22 ) =............?

Use following Excel command:

=T.DIST(t , df, cumulative)

=T.DIST(-1.22,19,TRUE)

=0.118696

=0.119

Thus P( t ≤ −1.22 ) = 0.119

Also we can use TI 84 plus calculator :

Press 2ND and VARS

Select tcdf(

Enter numbers:

Click on Paste and press Enter two times.

thus we get:

P( t ≤ −1.22 ) = 0.118696

P( t ≤ −1.22 ) = 0.119

Question 2)

a t distribution with 10 degrees of freedom. Find the value of c such that:

P(−c< t < c) = 0.90

Since area between -c to c is 0.90

then area in two tails = 1 - 0.90 = 0.10

Thus use following excel command:

=T.INV.2T(probability, df)

=T.INV.2T(0.10,10)

=1.812461

=1.812

thus c = 1.812

that is: P( -1.812 < t < 1.812)= 0.90

Use following steps inTI 84:

Press 2ND and VARS

Select invT(

Enter numbers:

Here we enter area in left tail = 0.10 / 2 = 0.05

thus

thus absolute value of c = 1.812