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Exercise

Cutoffs under the t-distribution

We can use the qt() function to find cutoffs under the t-distribution. For a given probability p and a given degrees of freedom df, qt(p, df) gives us the cutoff value for the t-distribution with df degrees of freedom for which the probability under the curve is p. In other words, if \(P(t_{df} < T) = p\), then \(T\) = qt(p, df). For example, if \(T\) corresponds to the 95th percentile of a distribution, \(p = 0.95\). The "middle 95%" means from p = 0.025 to p = 0.975.

Instructions
100 XP
  • Find the 95th percentile of the t-distribution with 10 degrees of freedom.
  • Find the cutoff value that bounds the upper end of the middle 95th percent of the t-distribution with 10 degrees of freedom.
  • Find the cutoff value that bounds the upper end of the middle 95th percent of the t-distribution with 100 degrees of freedom.
  • How do the last values probabilities compare? Based on your findings, is the middle 95% of the t-distribution wider for lower or higher degrees of freedom?