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.
Wheat=c( 5.2, 4.5, 6.0, 6.2, 6.8, 5.8)
Barley=c( 6.5, 8.0, 6.0, 7.5, 5.8, 5.6)
Maize=c( 5.7, 4.7, 6.3, 5.0, 5.9, 5.1)
Oats = c( 8.3, 6.2, 7.9, 6.9, 5.5, 7.1)
In this example I = and J =
What are the individual group means, x̅_i.?
x̅_Wheat =
x̅_Barley =
x̅_Maize =
x̅_Oats =
What is the grand mean x̅_..
x̅_.. =
Calculate the mean squared treatment. (Round your answer to two decimal places.)
MSTr = J/(I-1) ∑(x̅_i. - x̅_..)^2 =
Calculate the variance for each group. Note: These can be done in R using the var() command.
S^2_wheat =
S^2_Barley =
S^2_Maize =
S^2_Oats =
Calculate the mean squared error. (Round your answer to two decimal places.)
MSE = (S^2_1 + S^2_2 + ... + S^2_I) / I =
Does this data suggest that at least two of the grains differ with respect to true average thiamin content? Use a level α = 0.05 test based on the P-value method.
State the appropriate hypotheses.
H0: μ1 = μ2 = μ3 = μ4
Ha: all four μi's are unequal
H0: μ1 ≠ μ2 ≠ μ3 ≠ μ4
Ha: all four μi's are equal
H0: μ1 ≠ μ2 ≠ μ3 ≠ μ4
Ha: at least two μi's are equal
H0: μ1 = μ2 = μ3 = μ4
Ha: at least two μi's are unequal
Compute the test statistic value. (Round your answer to two decimal places.)
F = MSTr / MSE =