Question

4. In a packing plant, a machine packs cartons with jars. It is supposed that a new machine will pack faster on the average than the machine currently used. To test that hypothesis, the times it takes each machine to pack ten cartons are recorded. The results (machine.txt), in seconds, are shown in the following table. Each sample includes 10 observations New machine 42.1 41.3 | 41.0 41.8 Old machine 42.7 43.8 43. 6 433 43. 1 44.0 42.5 43.5 42.8 42 Do the data provide sufficient evidence to conclude that, on the average, the new machine packs faster? Perform the required hypothesis test at the 5% level of significance

Answer 1

y solution & no vero alata of New machine and old machine let the new machine be sample a and old machine be sample 2. Here Homes=Na Vs Hai Macha from data MAS 40 , X : 42.1441 +41-3 +41-8.4 14.2.4 + 42.87 43.2+ 42-3 +41-8 + 42.7 42 - 4 = 42104 => 42-14 2.0 2 ,: 10, Žoz 427 + 43.67 43.8 43.3 +42-5 +43.5+ 43.9 + melot at 44 of 44.4

3 2 3 m = 3,23 5:0-683 5250S (ma-1) si (tig-) 5,2 - 2 (20-)(0.6833" (10-1)(0.15 77 + 90+40-2 CO:466) *9(0.5625) 20-2 4.198 & 5.0625 20-2 9:260 18 > 0-5244 hest staletes t : Ii- ja 42:14-43-23 Vsp? ( a + 1 - - 0.514) otto) v0.5144 So-1028 0.32062 : - 3.39 df = ngxn2-2 ) 10+10. 2 18 At 5% L-o s sritical value : - 1.7342 Here to = -3.4 ao 1.7349 so Ropect to. There is so eindence that the new machine hacker faster