Assume that n = 10 and in Example 7 (Section 1.4). Find the most powerful randomized test of size a = 0.05. Suppose 8 is the percentage change in the yield of a process, under the effect of a very...

Assume that n = 10 and

in Example 7 (Section 1.4). Find the most powerful randomized test of size a = 0.05.

Suppose 8 is the percentage change in the yield of a process, under the effect of a very expensive new treatment. To obtain information about 8, we can observe i.i.d. K( 6,2500) observations, X_l, ... , X_n

(a) If n = 25,000,000 and x = 0.02, show that there is statistically significant evidence at the a = 0.05 level (one-tailed) that 8> O. Would it be wise to adopt the new treatment because of the strong evidence that it increases yield?

(b) If

show that there is not statistically significant evidence at the a = 0.1 level that 8> O. Does this imply that it would be wise not to adopt the treatment?