# Practice 8 Working with Student’s t Distribution in R

## 8.1 Directions

In this practice exercise, you will work with the Student’s t distribution R.

## 8.2 A closer look at the code

In this practice, you will learn about the pt() and qt() commands.

### 8.2.1 Let’s learn to use the pt() command

The pt() command has three arguments that we need to be concerned about.

• q which holds the value to find the probability of being less than or greater than
• df which holds the number of degrees of freedom
• lower.tail which is set to true for a less than calculation or false for a greater than calculation.

Student’s t-distribution has a mean of zero and a standard deviation of one. Here are a few examples.

# P(X <=  0.25) where X ~ t(20)
pt(q=0.25, df=20, lower.tail=T)
## [1] 0.5974313
# P(X >=  -0.1) where X ~ t(100)
pt(q=-0.1, df=100, lower.tail=F)
## [1] 0.5397277

### 8.2.2 Let’s learn to use the qt() command

The qt() command has three arguments that we need to be concerned about.

• p which holds the value for which you wish to find a probability.
• df which holds the number of degrees of freedom
• lower.tail which is set to true for a less than calculation or false for a greater than calculation.

Here is an example from the voice thread.

# Find the value of Z such that P(X <=  Z) = 25% where X ~ t(25)
qt(p=0.25, df=25, lower.tail=T)
## [1] -0.68443

## 8.3 R code used in the VoiceThread

# P(X <= 2.3) where X ~ t(5)
pt(q=2.3, df=5, lower.tail=T)

# Find the value of X such that the area to the left of X is 0.05 where X ~ t(46)
qt(p=0.05, df=46, lower.tail=T)

## 8.4 Now you try

Use R to complete the following activities (this is just for practice you do not need to turn anything in).

1. Find the value of Z P(Z >= 1) where Z ~ N(0,1)
2. Find the value of X such that P(X <= 70) = 25% where X ~ N(0,1)