a series of n Bernoulli trials is to be observed as data for testing $\displaystyle H_{0} : p = \frac{1}{2}$ versus $\displaystyle H_{1} : p > \frac{1}{2}$.

suppose that the null hypothese will be rejected only if k, the observed number of successes equals n.

for what value of p will the probability of making a Type II error equal 0.20?