Type the R transcript that shows the 97.5th percentile of t falling toward qnorm(0.975) as df runs 10, 30, 43, 1000.
Type the R transcript that shows the 97.5th percentile of t falling toward qnorm(0.975) as df runs 10, 30, 43, 1000.
Answer
> qt(0.975, c(10, 30, 43, 1000)) [1] 2.228139 2.042272 2.016692 1.962339 > qnorm(0.975) [1] 1.959964
qt takes a cumulative probability, so 0.975 leaves 2.5 % in the upper tail. By df 43 the value is 2.017, within 3 % of 1.960; the ∞ row is the limit.
IBS1 §8.1–8.2, CC BY 4.0; H-W7 (n = 44 example; the qt ladder converging to qnorm) — shape only; R output from a live Rscript session; original dataset