Question

What command do I use in R to compute the probability that a t distribution with 36 df exceeds 2.5 and then how do I compute the lower 10th percentile of a t distribution with 54 df (using what command in (R)?

Answer 1

Solution: 1) We need to find P(t > 2.5) when degrees of freedom is 36,

i.e. we need to find 1 - P(t < 2.5) , such that the area to the left of 2.5 is subtracted from 1 to find the required answer.

In R programming, the command pt(x,df) gives thearea to the left of 'x' under a Student's t-distribution with 'df' degrees of freedom.

so, the required answer is --> 1 - P(t < 2.5) = 1 -  0.9914431 = 0.008556915

The required R - code is --> 1 - pt(2.5,36)

2) The lower 10th percentile of a t-distrbution is the value of the variable such that the area to the left is 10%.

In R programming, the command qt(p,df) gives the value of the variable that has an area of "p" to the left under a t-distribution with "df" degrees of freedom.

So, the required answer = -1.297426

The required R-code is --> qt(0.10,54)

[The output for the answers are attached below for verification].