Statistical Test Review VII

Andy claims that $20\%$ of the public loves Quanteaser. Aaron dislikes Andy and wants to prove him wrong—specifically, he thinks Andy's estimate is too large. He takes a random sample of 100 people to test his claim. It turns out that 15 of the 100 people love Quanteaser, so Aaron argues that $15\%$ of the public loves Quanteaser. Compute, to the nearest thousandth, the value of $\beta$ for Aaron's alternative hypothesis under a $0.05$-level test (note that $z_{0.05} = -1.645$).