Question

DATA ANALYSIS FOR SYSTEMS ENGINEERING

Q / A packing plant purchases a new machine for wrapping jar. The new machine is expected to work faster than the older machines. To test this hypothesis, the working time for each machine to pack ten boxes were recorded. Results in seconds are shown in Table 1a below. Assume the variances are equal.

1. Perform a hypothesis test (6-steps procedure) at 5% significant and declare your decision.

2. Confirm the calculation by using Minitab or SPSS.

Table 1a : Packaging Time

New Machine					Old Machine
42.1	41.3	42.4	43.2	41.8	42.7	43.8	42.5	43.1	44
41	41.8	42.8	42.3	42.7	43.6	43.3	43.5	41.7	44.1

Answer 1

Seluition Ab ut bample ot bample machine Hene neuu 2 is old mrachune Ho l2 Hai li2 2 3 from the gvem data U2-19, =0.714 2mO-75 11-10/ o-53615 (0110-2 Tet tatustrc t u2.19-43-23 EI3.176 3615/70 d rt M 2 =10+10-2 = 16 A+ Sy. L0.s cutical Vahue is-1.734 Here cal t= -3.176 2 -I734 9raje dt Ho 6 Thare a a evidamce tar the So expectecd rachine s mer the der machine to cosik fastan ttam

Two-Sample T-Test and Cl: new, old Method Hmean of new Here P value 0.003 < 0.05 H: mean of old Difference: - H2 so, reject the null hypothesis Equal variances are assumed for this analysis. Descriptive Statistics Sample N Mean StDev SE Mean 10 42.190 0.714 0.23 new old 10 43.230 0.750 0.24 Estimation for Difference 95% Upper Bound for Difference Pooled Difference StDev 0.732 -0.472 -1.040 Test Null hypothesis Alternative hypothesis Hoi HH2 0 H- Ha < O T-Value DF P-Value -3.18 18 0.003