For a binomial distribution, the hypothesis $H_0: p = 0.2$ and $H_1: p\ne0.2$ are tested at the $10%$ level. $20$ trials are performed and the critical region is $X = 0$ or $X > 7$. Calculate the probability of a type II error and the power when the true value of $p$ is $0.3$:
My workings: $X - B(20, 0.3)$
The probability of a type II error is the probability of getting a result outside of the critical region when $p = 0.3$.
Hence $P(\text{Type II error}) = P(1 \le X \le 7)$
Hence $P = 0.771$
The textbook says $P = 0.772$, which is the $P X \ge 7$