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Exercise

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).

Instructions

100 XP
  • 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?