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 4 4.00 4.02 3.99 4.01 Machine 1 Machine 3 3.97 3.98 3.97 3.95 4.00 Machine 2 4.05 4.01 4.02 4.04 3.99 4.02 4.01 3.99 4.00 4.00 (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. (2). Transform the data MilkMachine.csv to the data set with one dependent variable and one independent variable as two separate columns. Import the dataset you created. Construct a One-way ANOVA model using correct R command. Inspect the model. What is the p value? What is the statistical decision?

Explanation / Answer

a)

The f-ratio value is 11.61262. The p-value is .000341. The result is significant at p < .01.

b)

# R CODE

##To load the data into MilkMachine

milkmachine <- read.csv ("MilkMachine.csv")

## command for anova test

results <- aov(Y ~ X, data=milkmachine)

P- value is 0.000341 < 0.01

Reject Ho

There is at least one group mean is different from the group.

Treatments 1 2 3 4 5 Total N 4 6 5 4 19 X 16.21 24.01 19.87 16.02 76.11 Mean 4.0525 4.0017 3.974 4.005 4.0058 X2 65.6945 96.0807 78.9647 64.1606 304.9005 Std.Dev. 0.034 0.0117 0.0182 0.0129 0.0332

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