Is it true that any interval of the form [x̄ − (s/√n)t, ∞) with a 90% quantile t is a 90% confidence interval?

Question

Accepted Answer

No. t = t_{n−1,0.9} under the convention t_{m,α} = (1−α)-th quantile That t is the 10th percentile, so the interval has coverage 10%, not 90%.

Any interval of the form $[\overset{ˉ}{X} - (S / n) t, \infty)$ with a 90% quantile t is a 90% confidence interval