Question

IdllCLLIS. 15. A company that makes processors for comput- ers uses a .05 significance level to reject any lot of processors that does not run at an average of 500 Millions of Instructions Per Second (MIPS). Twenty processors are selected at ran- dom to test the quality of six lots. Below are listed the resulting mean number of MIPS for each of the six lots of processors. Which lots should be rejected as having failed to meet quality standards? Specify the tcrit you will use for the tests as well as the tobs for each lot. Lot A: X = 502, s = 3.1 Lot B: X = 501.6, s = 3.3 Lot C: X = 499.6, s = 1.3 Lot D: X = 498.3, s = 2.6 Lot E: X = 501.4, s = 3.2 Lot F: X = 500.3, s = .6

Answer 1

Son - suppose w then nen Suppose we want to test Hoil=Mo Vs Hi : M & Mo a t-statistic to test the Ho is t= t-M - Vñ că-i) Sito a > t = n(X-Mo) Ntr under Hoi where s2 = 1 {(xi -3) 2 and we reject to at a-level of significance if itl>tn 1,42 otherwise we fail to reject Ho. (.e. accept Ho) for this given problem, we have Ho : M = 500 vs Hi: Mt 500 1. Mo = 500 ; n = 20; = 0.05 terit = tig, = 2.093 from the t-table. for lot A: = 502 , s=3.1 -In (x-Mo) = $20 (502-500) rzo (502-500) = 2120 3.1 3.1

I 31 tobe for lot A = 2520 - 2.885 Since [(toba) = 2805] >[tro 4= 2.013] & we reject Ho at &=0.05. le lat A has failed to meet quality standart for lot B: š = 502.6 Mo = 500 , S = 3.3 ,n=20 3.3 3.3 - 2.168 = (toba) g = (501.6–52) * J76 = V20x1.6 (toba) 6 = 2.168 since, [[tobe) = 2.168] > [ti, a = 2.093] we reject Ho Hence, lot & fails to meet quality standard. for lotc: x=499.6 , S=13 (tows) c = (499.6 - 500) 4520 1 (tos) c = -10376] - $20 * 10.4 1:3 = 1.3

2.6 2.6 " toba) el = 1376 (Itarit = 2.093) E > we fail to reject Ho (accept Ho) - l.e. lot c meet quality standard. for lot D Ã = 49813 s=2.6 (toba), = (493-3- 500)* 520 = - 17X170 (toks)o = - 2.924 ] • [ 1 (toba). I = 2.924] > [tot = 2.093] - we nogeet Ho re. lot fails to meet quality standard- for lot E x = 501.4, s= 3.2 .: (toks) = (5014-500) x 20 (tobs) E = 1.956 [(tos) = 1956] < [torit = 2:0937 we fail to reject Ho. (accept Hall 3.2 1.4 */20 3.2

1.e. lot E does not meet lot E does not m quality standard. 0.3*20 0.6 for lot F = 500.3, s= 0.6 i tobs) = (500.3 - 500)+850 (20 - 0.6 [{tokes) f = 2.236 . [(toba) p = 2.236] > [tomie = 2:013] we reject Ho at x = 0.05. e lot F does not meet quality standard. or lot f fail to meet quality standard.