SupposeY1, Y2, . . . , Y10is a random sample of sizen= 10 from a normal population with unknown meanand variance2= 4. It is known that the UMP test of

H0:=15versusHa:<15 has RR of the form{Y < k}. You need not prove this.

(a) Find the UMP test at level= 0.05. (b) Compute power(a) fora= 12.

(c) The RR{Y < k}from above can be rewritten in the form{z < k}withza standard normal random variable andka constant. Findk. (You'll see a familiar number.)