Suppose that a coin is biased, and the probability of a heads is one of the three values p = .2, .3, or .8. The coin is tossed repeatedly, and we let X be the number of tosses required to obtain the first head. To test Ho: p = .8, suppose we reject Ho if X > or equal to 3, and do not reject otherwise.
a) What is the probability of type I error, P[TI]?
b) What is the probability of a Type II error, P[TII], for each of the other two values to p?
c) For a test of Ho: p = .3, suppose we use a critical region of the form {1, 14, 15, ...}. Find P[TI], and also find P[TII] for each of the other values of p.