7. Let X be the number of successes in n independent trials with probability P of success, and let l/l(x) be the UMP test (9) for testing P s Po against P > Po at level of significance

a. (i) For n = 6, Po = .25 and the levels a = .05, .1, .2 determine C and y, and find the power of the test against PI = .3, .4, .5, .6, .7.

(ii) If Po = .2 and a = .05, and it is desired to have power p .9 against PI = .4, determine the necessary sample size

(a) by using tables of the binomial distribution,

(b) by using the normal approximation.* (iii) Use the normal approximation to determine the sample size required when a = .05, P= .9, Po = .01, PI = .02.