One Interval, Two Null Hypotheses

Neither test can be settled from the interval alone — a confidence interval carries no information about hypothesis tests.

$H_0: \mu = 20$ would be rejected only at $\alpha = 0.10$, not at $\alpha = 0.05$, because $20$ lies just outside the interval.

$H_0: \mu = 20$ is rejected ($|z| \approx 2.18$) while $H_0: \mu = 13$ is not ($|z| \approx 1.63$).

Both are rejected, since neither $20$ nor $13$ equals the point estimate $\bar{x} = 16$.