Question

3. A random sample of size 16 is drawn from a normal distribution with o = 9.0 for the purpose of testing: Ho : = 30 versus HP:ll # 30. The experimenter chooses to define the critical region C to be the set of sample means lying in the interval (29.9, 30.1). (3.1) What level of significance does the test have? (3.2) Improve the test by changing the definition of C, assuming the same a is to be used.

Answer 1

50.9 A simple ore 16 som rendom sample na 16 xu Ncu, 6) xun(309,0) Hypothesin Hoiu-30 Hu 230 Vis Test statistics (2coll - x-u u Nr4,62) ban Here ž in the intewel rearon a set sample mean bying in the (29.9, 30.1) If toling x = 29.9 Real - 29.9.30 9.0/ I 16 Izcall 0.04h toking x = 30.1 if 20 - 3011-30 Grofits 2co - 0.1 2.25 2 col = 0.04h - 0.044

π so test statistics we toking volve some any 50 Acceptance Region Rejecten Region 24 (1-2) 2 we tole & a 0.05 t. Louis significance Decision then Rule : Repeat If l2coll > He at 57 2 table L-05 2 table value 2 2 0.05 2 table = 0.4800 2 2 x p(xcx) 0x0.480 = 0.96 toble

L.org. 12 cell C 2 tuble Accept to at 5-1 coll aghha ora 6 cal L seble و 20 كان Accent H. at 5 .1 Lower conclusion in an critical Region c to I be the set sample meen olging in interval (29.3, 30.1 Accepting to so a = 30 En whole hole critica Region u=30 Accepted