Probabilities under the t-distribution
We can use the pt() function to find probabilities under the t-distribution. For a given cutoff value q and a given degrees of freedom df, pt(q, df) gives us the probability under the t-distribution with df degrees of freedom for values of t less than q. In other words, \(P(t_{df} < T)\) = pt(q = T, df).
This exercise is part of the course
Inference for Numerical Data in R
Exercise instructions
- Find the probability under the t-distribution with 10 degrees of freedom below \(T = 3\).
- Find the probability under the t-distribution with 10 degrees of freedom above \(T = 3\).
- Find the probability under the t-distribution with 100 degrees of freedom above \(T = 3\).
- How do the last two probabilities compare? Why?
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# P(T < 3) for df = 10
(x <- pt(___, df = ___))
# P(T > 3) for df = 10
(y <- ___)
# P(T > 3) for df = 100
(z <- ___)
# Comparison
y == z
y > z
y < z