Largest count of fans that rejects a 20 percent claim

Alice says $20\%$ of people love Spotify; Bob suspects the true share is lower. He surveys $100$ random people and runs a one-sided large-sample z-test at $\alpha=0.05$ (critical value $-1.645$). What is the largest number of Spotify lovers in his sample that still lets him reject Alice's claim?

$13$. Under $H_0$ the sample proportion has standard error $\sqrt{0.2\cdot0.8/100}=0.04$. Rejection needs $\hat p<0.2-1.645\times0.04=0.1342$, i.e. at most $13$ people out of $100$.