Six samples of each of four types of cereal grain grown in a certain region were

Question

Six samples of each of four types of cereal grain grown in a certain region were analyzed to determine thiamin content, resulting in the following data (µg/g): Note: If you want to use R this data has been set up so you may copy it directly into R.

1. In this example i = _____ J =_____

.

2. What are the individual group means, xi.? ( xi mean )

x Wheat =____

x Barley =____

x Maize = ____

x Oats =_____

.

3. What is the grand mean x..?

x.. =_____

.

4. Calculate the mean squared treatment. (Round your answer to two decimal places.)

MSTr = ______

.

5. Calculate the variance for each group. Note: These can be done in R using the var() command.

S2wheat =

S2Barley =

S2Maize =

S2Oats =

6. Calculate the mean squared error. (Round your answer to two decimal places.)

MSE= _____

.

7. Compute the test statistic value.(Round your answer to two decimal places.)

Wheat=c( 5.3, 4.6, 6.1, 6.2, 6.8, 5.7) Barley=c( 6.4, 7.9, 6.0, 7.5, 5.9, 5.7) Maize=c( 5.9, 4.8, 6.4, 4.9, 5.9, 5.2) Oats = c( 8.2, 6.0, 7.8, 7.1, 5.5, 7.1) MST T MSE

Explanation / Answer

for above data:

1)i=4 ; j=6

2)group means :

3) grand mean =37.225

4)MSTr=2.6749

5)

6) MSE=0.73

7)F=3.68

Groups Count Sum Average Variance Wheat 6 34.7 5.783333 0.589667 Barley 6 39.4 6.566667 0.838667 Maize 6 33.1 5.516667 0.413667 Oats 6 41.7 6.95 1.067 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 8.024583 3 2.674861 3.678049 0.029366 3.098391 Within Groups 14.545 20 0.72725 Total 22.56958 23

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