8. (i) Let X have binomial distribution b( p, n), and consider testing H : p = Po at level a against the alternatives OK :r/« S }Po/qo or 2po/qo . For a = .05 determine the smallest sample size for which there exists a test with power ~.8 against OK if Po = .1, .2, .3, .4, .5. (ii) Let Xl' " '' Xn be independently distributed as Na, (12). For testing (1 = 1 at level a = .05, determine the smallest sample size for which there exists a test with power .9 against the alternatives (12 S } and (12 2. [See Problem 5 of Chapter 4.)