Question

Consider a random variable T that has a t-distribution with k = 16 degrees of freedom. What is P(T > 1.8)?

Group of answer choices

0.0454

0.9546

0.2499

0.4742

0.8000

Answer 1

We have given T distribution

degree of freedom = k = 16

We have to find P (T > 1.8 )

We either use Ti -83 , Ti -84 calculator or Excel

Excel

">" sign means right side area that means 1 tail area

Excel command

Select empty box from excel

=TDIST(1.8 , 16 , 1 )

Do not forget to type = sign while using excel

Press " enter "

We get probability as 0.045371615

For Ti -84 or Ti -83 calculator

Press " 2ND" key

Press " VARS "

Select "tcdf "

Lower = 1.8

Upper = 10000000    ( We plug upper as large positive number because we have to find right side probability )

df =   16                   ( degrees of freedom )

That is

tcdf( 1.8 , 10000000 , 16 )

We get the probability as 0.0453716152

We round probability up to 4 decimal place

P(T > 1.8) = 0.0454

Note : we can't use T table because it do not provide the exact value for the probability.

Final answer :-

First choice is correct

P(T > 1.8) = 0.0454