3. A milk company has four machines that fill gallon jugs with milk. The quality

Question

3. A milk company has four machines that fill gallon jugs with 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. Machine 2 3.99 4.02 4.01 3.99 4.00 4.00 Machine 1 Machine 3 Machine 4 4.05 4.01 4.02 4.04 3.97 3.98 3.97 3.95 4.00 4.00 4.02 3.99 4.01 (1). Given SST 0.010579 and SSC 0.007076, use a .01 to manually test the hypotheses whether the average fill for these machines is the same.

Explanation / Answer

MS = SS/df

SS_within = SST - SSC

df_between = r-1 = 4-1    { r is the number of column}

df_total = n-1= 19-1 = 18

F = MS_between/MS_within

p-value = 0.00068 < 0.01

we reject the null hypothesis

ANOVA Source of Variation SS df MS F P-value F crit Between Groups 0.007075614 3 0.002358538 10.09840252 0.000685335 3.2873821 Within Groups 0.003503333 15 0.000233556 Total 0.010578947 18

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