A milk company has four machines that fill gallon jugs of milk. The quality cont
ID: 3338178 • Letter: A
Question
A milk company has four machines that fill gallon jugs of milk. The quality control manager is interested in determining whether the average fill for these machines is the same. The following data represent random samples of fill measures (in quarts) for 19 jugs of milk filled by the different machines. Using a significance level of 1%, develop an ANOVA to determine if the average fill for these machines is the same.
Machine 1
Machine 2
Machine 3
Machine 4
7
9
9
10
8
10
10
11
9
11
11
11
10
12
11
12
The observed value of the F statistic is ____
Machine 1
Machine 2
Machine 3
Machine 4
7
9
9
10
8
10
10
11
9
11
11
11
10
12
11
12
Explanation / Answer
Step 1
Null Hypothesis Ho : µ1 =µ2 =µ3 =µ4
Alternative Hypothesis : atleast one machine is diffrent
Step 2
Degrees of freedom between = k - 1 = 4 - 1 = 3
Degrees of freedom Within = n - k = 16 - 4 = 12
Degrees of freedom Total F( k-1,n - k,) at 0.01 is = F Crit = 5.953
Step 3
Grand Mean = G / N = 8.5+10.5+10.25 +11 / 4 = 10.063
SST = ( Xi - GrandMean)^2 = (7-10.063)^2 + (8-10.063)^2 + (9-10.063)^2 + ……..& so on = 23.426
SS Within = (Xi - Mean of Xi ) ^2 =,(7-8.5)^2 + (8-8.5)^2 + (9-8.5)^2 + ……..& so on = 12.75
SS Between = SST - SS Within = 23.426 - 12.75 = 10.676
Step 4
Mean Square Between = SS Between / df Between = 10.676/3 = 3.559
Mean Square Within = SS Within / df Within = 12.75/12 = 1.063
Step 5
F Cal = MS Between / Ms Within = 3.559/1.063 = 3.349
We got |F cal| = 3.349 & |F Crit| =5.953
MAKE DECISION
Hence Value of |F cal| < |F Crit|and Here We Accept Ho
we conclude that the average fill for these machines is the same.
Treatments ONE WAY ANOVA Mean = X /nMachine 1 7 8 9 10 8.5
Machine 2 9 10 11 12 10.5
Machine 3 9 10 11 11 10.25
Machine 4 10 11 11 12 11
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