Question

Use the calculator provided to solve the following problems.

Consider a t distribution with 16 degrees of freedom. Compute P (t ≥ 1.10)
Round your answer to at least three decimal places.

Consider a t distribution with 28 degrees of freedom. Find the value of c such that P(-c < t < c) =0.99
Round your answer to at least three decimal places.

P (t ≥1.10) =

c=

Answer 1

Solution:

We have to use the calculator to solve the following problems. thus we will use TI 84 plus calculator.

Part 1) a t distribution with 16 degrees of freedom. Compute P (t ≥ 1.10)

Use following steps in TI 84 plus calculator.

1) Press 2ND

2) Press VARS

3) select tcdf(

Lower: 1.10

Upper : 9999999999999 ( Type very large number, so that we can assume upper limit is infinity)

df: 16

Paste

Click on Paste and press Enter two times.

We get: 0.1438

Thus

P (t ≥ 1.10) = 0.1438

P (t ≥ 1.10) = 0.144

Part 2) a t distribution with 28 degrees of freedom. Find the value of c such that P(-c < t < c) =0.99

Since 0.99 is area between -c to c , then area in two tails is 1- 0.99 = 0.01

Thus area in left tail = 0.01/2=0.005

Thus use 0.005 to find value of -c.

Use following steps in TI 84 plus calculator:

1) Press 2ND

2) Press VARS

3) select invT(

enter following numbers:

Area = 0.005

df = 28

Paste

Click on Paste and press Enter two times:

we get:

-2.763

That is: -c = -2.763 , then c = 2.763

Thus c = 2.763