#small-samples

Question 1: Single choice

With $N = 2$ samples per dataset you build 100 intervals $\hat{\mu} \pm t^*\hat{\sigma}/\sqrt{N}$ with $t^* = 1$ (a 50% confidence interval for $N = 2$ ), where the true mean is 0. About half of them contain 0, and some very short intervals lie far from 0. Does this contradict the 50% interpretation?

No: 50% describes the procedure over many datasets; a short interval just means the two samples were close1
Yes: every observed 50% interval, the short ones included, should contain 0 with probability exactly one half2
Yes: short intervals come from precise estimates, so they should cover the mean more often3
No, but only because $t^* = 1$ is too small for $N = 2$ , so the real coverage is just 25%4

Timed test