An experiment was conducted to compare the filling capability of packaging equip

Question

An experiment was conducted to compare the filling capability of packaging equipment at two different bottling plants. Ten bottles were randomly selected from Plant 1 and the fill volume measured and ten bottles were randomly selected from Plant 2 and the fill volume measured. It is known that fill volume is normally distributed. The data below is the fill volume, in milliliters:

    Plant 1                         Plant 2

755      751                  756      750

753      753                  759      756

752      753                  755      756

753      754                  756      755

752      751                  755      756

      Perform an appropriate hypothesis test to determine whether Plant 2 is producing an average fill volume that is larger than that of Plant 1. Use = 0.02.

Explanation / Answer

here

hence degree of freedom : v=((s12/n1+S22/n2)2/((s12/n1)2/(n1-1) +(s22/n2)2/(n2-1) ) =14 (rounding it down)

and std error =(s12/n1+S22/n2)1/2=0.806

hence test stat t =(x1-x2)/std error =-3.3489

for which p value =0.002

as p value is less then 0.02 level, we reject that mean are equal and accept the claim that Plant 2 is producing an average fill volume that is larger than that of Plant 1

S. no plant 1 plant 2 1 755 756 2 753 759 3 752 755 4 753 756 5 752 755 6 751 750 7 753 756 8 753 756 9 754 755 10 751 756 total 7527.000 7554.000 mean 752.700 755.400 std deviation(S) 1.252 2.221

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